Papers by David Eisenbud

1969


1. Groups of order automorphisms of certain homogeneous ordered sets, Mich. Math. J. 16 (1969) 59--63.
   
   1970
   
   
2. Subrings of Artinian and Noetherian Rings, Math.~Ann.~185 (1970) 247--249.
   
   
3. Modules over Dedekind Prime Rings (with J.~C.~Robson), J.~Alg.~16 (1970) 67--85.
   
   
4. Hereditary Noetherian Prime Rings (with J.~C.~Robson), J.~Alg.~16 (1970) 86-- 104.
   
   1971
   
   
5. Serial Rings (with P.~A.~Griffith), J.~Alg.~17 (1971) 389--400.
   
   
6. The Structure of Serial Rings (with P.~A.~Griffith), Pacific Journal of Math.~ 36 (1971) 109--121.
   
   1972
   
   
7. Lifting Modules and a Theorem on Finite Free Resolutions (with D.~A.~ Buchsbaum), in {\bf Ring Theory}, Park City 1971, Academic Press (1972) 63--74.
   
   
8. Basic Elements; Theorems from Algebraic K-Theory (with E.~G.~Evans), Bull.~ AMS 78 (1972) 546--549.
   
   1973
   
   
9. What Makes a Complex Exact? (with D.~A.~Buchsbaum), J.~of Alg., 25 (1973) 259--268.
   
   
10. Remarks on Ideals and Resolutions (with D.~A.~Buchsbaum), Symposia Math.~ XI, Academic Press, London (1973) 193--204.
    
    
11. Generating Modules Efficiently; Theorems from Algebraic K-Theory \ (with E.~G. Evans), J.~Alg.~27 (1973) 278--305.
    
    
12. Every Algebraic Set in $n$-Space is the Intersection of $n$ Hypersurfaces (with E.~G. Evans), Invent.~Math.~19 (1973) 107--112.
    
    
13. On a Problem in Linear Algebra (with D.~A.~Buchsbaum), Proc.~of the Kansas Conference on Commutative Rings, Springer Lect.~Notes 311 (1973) 50--56.
    
    
14. Three Conjectures on Modules over Polynomial Rings (with E.~G.~Evans), Springer Lect.~Notes in Math.~311 (1973) 78--89.
    
    1974
    
    
15. Some structure theorems for finite free resolutions (with D.~A.~Buchsbaurm), Adv.~in Math.~12 (1974) 84--139.
    
    
16. Adic approximation of complexes, and multiplicities, Nagoya Math.~J.~54 (1974) 61--67.
    
    1975
    
    
17. A survey of some results on free resolutions, {\bf Proc.~International Congress of Mathematicians, Vancouver, 1974} (1975) 303--308.
    
    
18. Generic Free Resolutions and a Family of Generically Perfect Ideals (with D.~ A.~Buchsbaum), Adv.~in Math.~18 (1975) 245--301.
    
    
19. Some directions of recent progress in commutative algebra, in {\bf Proceedings of Symposium on Algebraic Geometry, Arcata 1974}, Proc.~of Symposia in Pure Math. 29, Amer.~Math.~Soc.~(1975).)
    
    
20. Notes on the topological degree of a smooth mapping, in {\bf Conf.~on Commutative Alg.~1975}, Queen's papers on Pure and Appl.~Math.~42 (1975) 70-- 79.
    
    1976
    
    
21. The Topological degree of a finite $C^{\infty}$ map germ (with H.~Levine) in {\bf Structural Stability, the Theory of Catastrophes, and Applications in the Sciences}, Springer Lect.~Notes in Math.~525.
    
    
22. A Generalized Krull Principal Ideal Theorem (with E.~G.~Evans, Jr.), Nagoya Math.~J. 62 (1976) 41--53.
    
    1977
    
    
23. Algebra structures for free resolutions and structure theorems for ideals of codimension 3 (with D.~A.~Buchsbaum), Amer.~J.~of Math.~99 (1977) 447--485.
    
    
24. What annihilates a Module? (with D.~A.~Buchsbaum), J.~Alg.~47 (1977) 231--243.
    
    
25. An algebraic formula for the degree of a $C^{\infty}$ map germ (with H.~Levine), Annals of Math.~106 (1977) 19--44.
    
    
26. Remarks on Regular Sequences, (with M.~Herman W.~Vogel), Nagoya Math.~J.~ 67 (1977) 177--180.
    
    
27. Enriched free resolutions and change of rings, in {\bf S\'em\-inaire d'Alg\-\`ebre Paul Du\-breil 1975-76}, Springer Lect.~Notes in Math.~(1977) 1--8.
    
    
28. Solution du probleme de Serre par Quillen-Suslin, in {\bf S\'eminaire d'Alg\`ebre Paul Dubreil 1975--76}, Springer Lect.~Notes in Math.~(1977) 9--19.
    
    1978
    
    
29. An Algebraic Approach to the Topological Degree of a $C^{\infty}$ Map, Bull.~Amer.~ Math. Soc. 84 (1978) 751--764.
    
    1979
    
    
30. A Nullstellensatz with Nilpotents (with M.~Hochster), J.~Alg.~58 (1979) 157-- 161.
    
    
31. On the number of generators of ideals in local Cohen-Macaulay rings (with M.~Boratynski and D.~Rees), J.~Alg.~57 (1979) 77--81.
    
    1980
    
    
32. Introduction to algebras with straightening laws, in{\bf Ring Theory and algebra III, Norman Oklahoma 1979}, Lect.~Notes in pure and appl.~Math., Marcel Dekker, New York (1980) 243--268
    
    
33. Homological Algebra over a Complete Intersection, Trans.~Am.~Math.~Soc.~260 (1980), 35--63.
    
    
34. Young Diagrams and Determinantal Varieties (with C.~Procesi and C.~ DeConcini), Invent.~Math.~56 (1980) 129--165.~
    
    
35. Transcanonical embeddings of Hyperelliptic curves, J.~Pure and Applied Alg.~ 19 (1980) 77--83.
    
    1981
    
    
36. On the normal bundles of smooth rational space curves (with A.~Van de Ven), Math. Ann. 256 (1981) 453--463.
    
    
37. Projective resolution of Cohen-Macaulay Algebras (with O.~Riemenschneider and F.-O.~Schreyer), Math.~Ann.~257 (1981) 85--98.
    
    
38. Transverse foliations of Seifert bundles and self-homeomorphisms of the circle (with Ulrich Hirsch and Walter Neumann), Comm.~Math.~Helv.~56 (1981) 638--660.
    
    
39. Report on the normal bundles of curves in ${\bf P}^3$, in {\bf S\'eminaire Paul Dubreil et Marie-Paul Malliavin 1980}, Springer Lect.~Notes in Math.~867 (1981) 141--147.
    
    1982
    
    
40. Projective summands in generators (with R.~Wiegand and W.~Vasconcelos), Nagoya Math.~J.~86 (1982) 203--209.
    
    
41. On the variety of smooth rational space curves with given degree and normal bundle (with A.~Van de Ven), Inv.~Math.~67 (1982) 89--100.
    
    
42. Curves of almost maximal genus (with J.~Harris), in {\bf Curves in Projective Space}, Presses de l'Univ.~de Montreal (1982) 81--131.
    
    1983
    
    
43. Cohen-Macaulay Rees algebras and their specialization (with C.~Huneke), J.~ Alg.~81 (1983) 202--224.
    
    
44. Rational curves with cusps, in {\bf Singularities, Arcata}, Symposia in Pure Mathematics of the American Mathematical Society Vol.~40, (1983) 337--344.
    
    
45. Divisors on general curves and cuspidal rational curves (with J.~Harris), Invent. Math. 74 (1983) 371--418.
    
    
46. A simpler proof of the Gieseker-Petri Theorem (with J.~Harris), Invent.~Math.~ 74 (1983) 269--280.
    
    
47. On the Brill-Noether Theorem, in {\bf Open Problems in Algebraic Geometry}, Springer L.~N.~Math.997 (1983) 131--137.
    
    1984
    
    
48. Linear free resolutions and minimal multiplicity (with S.~Goto), J.~Alg.~88 (1984) 89--133.
    
    
49. Limit linear series, the irrationality of $M_g$, and other applications, Bull.~AMS 10 (1984) 277--280.
    
    1985
    
    
50. Recent progress in the study of Weierstrass points (with J.~Harris), in {\bf Geometry Today}, Birkhauser Boston, Progress in Math.~60 (1985) 121--127.
    
    1986
    
    
51. Limit linear series: basic theory (with J.~Harris), Invent.~Math.~85 (1986) 337--371.
    
    1987
    
    
52. On varieties of minimal degree (a centennial account), (with J.~Harris), in {\bf Algebraic Geometry, Bowdoin 1985}, Symposia in Pure and App.~ Math.~46 (1987) 1--14.
    
    
53. Existence, decomposition, and limits of certain Weierstrass points (with J.~Harris), Invent.~Math.~87 (1987) 495--515.
    
    
54. The monodromy of Weierstrass points (with J.~Harris), Invent.~Math.~90 (1987) 333--341.
    
    
55. When ramification points meet (with J.~Harris), Invent.~Math.~87 (1987) 485--493.
    
    
56. The irreducibility and monodromy of some families of linear series (with J.~ Harris), Ann.~Sci.~de l'Ec.~Norm.~Sup.~20 (1987) 65--87.
    
    
57. The Kodaira dimension of the moduli space of curves of genus $\geq 23$ (with J.~Harris), Invent.~Math.~90 (1987) 359--387.
    
    
58. Cohen-Macaulay Modules on quadrics (with R.-O.Buchweitz and J.~Herzog), Springer Lect.~Notes in Math.1273 (1987) 58--116.
    
    
59. On the resiliency of determinantal ideals, in {\bf Commutative Algebra and Combinatorics (Kyoto, 1985)} 29--38 (1987), North-Holland, Amsterdam.
    
    1988
    
    
60. The classification of homogeneous Cohen-Macaulay rings of finite Cohen- Macaulay type, (with J.~Herzog), Math.~Ann.~280 (1988) 347--352.
    
    
61. Determinantal equations for curves of high degree (with J.~Koh and M.~Stillman), Am.~J.~Math.~110 (1988) 513--539.
    
    
62. Linear Sections of Determinantal Varieties, Am.~J.~Math.~110 (1988) 541--575.
    
    
63. Vector spaces of matrices of low rank (with J.~Harris), Adv.~in Math.~70 (1988) 135--155.
    
    
64. Varieties cut out by quadrics: scheme-theoretic versus homogeneous generation of ideals (with Lawrence Ein and Sheldon Katz), in {\bf Algebraic Geometry, Sundance 1986}, Springer Lect.~Notes 1311, ed.~A.~Holme and R.~ Speiser.~pp.~51--71 (1988).
    
    1989
    
    
65. Remarks on points in a projective space (with J.~Koh), in {\bf Commutative Algebra, Berkeley}, Math.~Sci.~Res.~Inst.~Publ.~15, Springer Verlag NY (1989) 157--173.
    
    
66. Rank Varieties of Matrices (with D.~Saltman), in {\bf Commutative Algebra, Berkeley}, Math.~Sci.~Res.~Inst.Publ.~15, Springer Verlag NY (1989) pp.~173--213.
    
    
67. Progress in the theory of Algebraic Curves (with J.~Harris), Bull.~AMS 21 (1989) 205--232.
    
    
68. The Clifford dimension of a projective curve (with H.Lange, G.~Martens, and F.-O.~Schreyer) Compositio Math.~72 (1989) 173--204.
    
    
69. Irreducibility of some families of linear series (with J.~Harris), Ann.~Sci.~l'Ec.~Norm. Sup.~22 (1989) 33--53.
    
    1990
    
    
70. Ideals with a regular sequence as syzygy, appendix (with C.~Huneke) to ``Sur les hypersurfaces dont les sections hyperplanes sont a module constant'', by Arnaud Beauville, in {\bf The Grothendieck Festschrift}, Vol.~I, Progress in Math.~86 (1990) 121--133, Birkhauser Boston.
    
    1991
    
    
71. On the Hurwitz scheme and its monodromy (with N.~Elkies, J.~Harris, and R.~Speiser), Compositio Math.~77 (1991) 95--117.
    
    
72. Some linear syzygy conjectures (with J.~Koh), Adv.~in Math.~(1991) 47--76.
    
    
73. Graph curves (with D.~Bayer), Advances in Math.~86 (1991) 1--40.
    
    1992
    
    
74. Direct methods for primary decomposition (with C.~Huneke and W.~Vasconcelos) Invent.~Math.~110 (1992) 207--235.
    
    
75. Finite projective schemes in linearly general position (with J.~Harris) Journal of Algebraic Geometry 1 (1992) 15--30.
    
    
76. An excess intersection formula, and some applications (with J.~Harris), Journal of Algebraic Geometry 1 (1992) 31--60.
    
    
77. The dimension of the Chow variety of curves (with J.~Harris), Compositio Math.~83 (1992) 291--310.
    
    
78. Green's Conjecture: An orientation for algebraists, in {\bf Proceedings of the Sundance conference in Free Resolutions in Commutative Algebra and Algebraic Geometry, Suncance 90}, (ed.~David Eisenbud and C.~Huneke), Jones and Bartlett, Boston (1992) 51--79.
    
    
79. Regularity of modules over a Koszul Algebra (with L.~L.~Avramov) Journal of Algebra 153 (1992) 85--90.
    
    1993
    
    
80. Open Problems in Computational Algebraic Geometry and commutative Algebra, in {\bf Computational Algebraic Geometry and Commutative Algebra, Cortona 1991}, (ed.~D.~Eisenbud and L.~Robbiano) Cambridge University Press, Cambridge, England, (1993) 49--71.
    
    
81. Higher Castelnuovo Theory (with M.~Green and J.~Harris), in {\bf Journ\'ees de g\'eom\'etrie Alg\'ebrique d'Orsay}, Ast\'erisque 218 (1993) 187--202.
    
    1994
    
    
82. Juggling drops and descents (with J.~Buhler, R.~Graham, and C.~Wright). American Math.~Monthly (1994) 507--519.
    
    
83. Nets of skew forms and the linear syzygy conjecture, (with Jee Koh).~Adv.~in Math.~106 (1994) 1--35.
    
    
84. Finding sparse systems of parameters, (with B.~Sturmfels) J.~of Pure and Appl.~Alg.~94 (1994) 143--157.
    
    
85. Ideals of minors in free resolutions, (with M.~Green) Duke J.~Math. 75 (1994) 339--352.
    
    
86. Initial ideals of Veronese subrings, (With A.~Reeves and B.~Totaro) Advances in Math. 109 (1994) 168--187.
    
    1995
    
    
87. Ribbons and their canonical embeddings, (with D.~Bayer) Trans.~Am.~Math.~Soc.~347 (1995) 719--756.
    
    
88. Clifford indices of ribbons, (with M.~Green) Trans.~Am.~Math.~Soc.~347 (1995) 757--765.
    
    1996
    
    
89. Binomial ideals (with B.~Sturmfels), Duke Math.~J.~84 (1996) 1--45.
    
    
90. Cayley-Bacharach Theorems and Conjectures (with M.~Green and J.~Harris), \goodbreak Bull.~Amer.~Math.~Soc.33 (1996) 295--324.
    
    1997
    
    
91. Evolutions, Symbolic Squares, and Fitting Ideals (with B.~Mazur), J. Reine Angew. Math. 488 (1997), 189--201.
    
    
92. Modules that are Finite Birational Algebras (with B.~Ulrich) Illinois J. Math. 41 (1997) 10--15.
    
    1998
    
    
93. Noncommutative Gr\"obner bases for commutative ideals (with I.~Peeva and B.~Sturmfels), Proc. Amer. Math. Soc. 126 (1998), no. 3, 687--691.
    
    
94. Computing cohomology.~Chapter of ``Computational methods in Commutative Algebra and Algebraic Geometry'' by ~W.~Vasconcelos, Springer Verlag, Berlin, 1998.
    
    
95. Chains of maps between indecomposable modules (with J.~A.~de la Pe\~na), J. Reine Angew. Math. 504 (1998), 29--35.
    
    
96. Lattice walks and primary decomposition (with P.~Diaconis and B.~Sturmfels), Mathematical essays in honor of Gian-Carlo Rota (Cambridge, MA, 1996), 173--193, Progr. Math., 161, Birkhäuser Boston, Boston, MA, 1998.
    
    1999
    
    
97. Gale Duality and Free Reolutions of ideals of points (with S.~Popescu) Invent. Math. 136 (1999) 419--449.
    
    
98. Syzygy ideals for determinantal ideals and the syzygetic Castelnuovo lemma (with Sorin Popescu). Commutative algebra, algebraic geometry, and computational methods (Hanoi, 1996), 247--258, Springer, Singapore, 1999.
    
    2000
    
    
99. The projective geometry of the Gale transform (with S.~Popescu), J. Algebra 230 (2000) 127--173.
    
    
100. Cohomology on toric varieties and local cohomology with monomial supports. (with Mircea Mustata, and Mike Stillman). In Symbolic computation in algebra, analysis, and geometry (Berkeley, CA, 1998). J. Symbolic Comput. 29 (2000) 583--600.
     
     
101. Enriques Surfaces and other Non-Pfaffian Subcanonical Subschemes of Codimension 3 (with Charles Walter, and Sorin Popescu). Special issue in honor of Robin Hartshorne. Comm. Algebra 28 (2000) 5629--5653.
     
     2001
     
     
102. Hilbert functions, residual intersections, and residually ${\rm S}\sb 2$ ideals (with Marc Chardin and Bernd Ulrich). Compositio Math. 125 (2001), no. 2, 193--219.
     
     
103. Appendix to ``Jet schemes of locally complete intersection canonical singularities,'' by Mircea Musta\c t \u a (with Edward Frenkel.) Invent. Math. 145 (2001), no. 3, 397--424.
     
     
104. Lagrangian subbundles and codimension 3 subcanonical subschemes (with Sorin Popescu and Charles Walter). Duke Math. J. 107 (2001), no. 3, 427--467.
     
     
105. A simple proof of some generalized principal ideal theorems (with Craig Huneke and Bernd Ulrich). Proc. Amer. Math. Soc. 129 (2001), no. 9, 2535--2540.
     
     2002
     
     
106. Exterior algebra methods for the minimal resolution conjecture (with Sorin Popescu, Frank-Olaf Schreyer, and Charles Walter). Duke Math. J. 112 (2002), no. 2, 379--395.
     
     
107. Projective Geometry and Homological Algebra. Expository chapter, pp.~18--40 in Computations in Algebraic Geometry with Macaulay 2 David Eisenbud, Daniel R.~Grayson and Bernd Sturmfels (Eds.) Springer Verlag Berlin Heidelberg 2002.
     
     
108. Sheaf algorithms using the exterior algebra (with Wolfram Decker). pp.~215--250 in Computations in Algebraic Geometry with Macaulay 2 David Eisenbud, Daniel R.~Grayson and Bernd Sturmfels (Eds.) Springer Verlag Berlin Heidelberg 2002.
     
     
109. Periodic resolutions over exterior algebras. J. Algebra {\bf 258} (2002), no.~1, 348--361
     
     2003
     
     
110. Resultants and Chow forms via exterior syzygies. (with F.-O. Schreyer\ and\ J. Weyman). J. Amer. Math. Soc. {\bf 16} (2003), 537--579.
     
     
111. What is the Rees algebra of a module? (with C. Huneke\ and\ B. Ulrich). Proc. Amer. Math. Soc. {\bf 131} (2003), no.~3, 701--708
     
     
112. An Exterior View Of Modules And Sheaves. In {\it Advances in Algebra and Geometry, University of Hyderabad Conference 2001}, ed. C. Musili. Hindustan Book Agency (2003) 209--217.
     
     
113. Hyperplane arrangement cohomology and monomials in the exterior algebra (with Sorin Popescu and Sergey Yuzvinsky.) Trans. Amer. Math. Soc. 355 (2003), 4365-4383.
     
     
114. Sheaf cohomology and free resolutions over exterior algebras (with Gunnar FlC8ystad and Frank-Olaf Schreyer). Trans. Amer. Math. Soc. 355 (2003), 4397-4426.
     
     
115. Fitting's Lemma for -graded modules (with Jerzy Weyman). Trans. Amer. Math. Soc. 355 (2003), 4451-4473.
     
     
     
     
     
     Accepted or submitted
     
     
116. Heights of Ideals of Minors. David Eisenbud, Craig Huneke, Bernd Ulrich. 20 pages. Math. Annalen., to Appear
     
     
117. Order Ideals and a Generalized Krull Height Theorem. David Eisenbud, Craig Huneke, Bernd Ulrich. 20 pages. American Journal of Math., to Appear.
     
     
118. A Note on Veronese Intersections (with Klaus Hulek and Sorin Popescu) math.AG/0302167 (submitted)
     
     
     
     
     
     In Preparation
     
     
119. The Geometry of Syzygies. (Graduate textbook, to appear as a Springer Graduate Text in Mathematics, 2004).
     
     
120. Symmetric locally free resolutions of coherent sheaves (with Sorin Popescu, and Charles Walter)
     
     
121. Computing the Hilbert function of a good residual intersection (with Marc Chardin and Bernd Ulrich)
     
     
122. Restricting linear syzygies (with Mark Green, Klaus Hulek, Sorin Popescu, William Oxtoby)
     
     
123. Linearly Presented Ideals (with Craig Huneke and Bernd Ulrich)
     
     
124. F.S.~Macaulay. (History of Math) with Jeremy Gray.
     
     
125. Order ideals of torsion free modules (with Craig Huneke and Bernd Ulrich).
     
     
126. A Second Course in Algebraic Geometry. Graduate textbook. With Joe Harris.