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Classical Algebraic Geometry Today |
| January 26, 2009 to January 30, 2009 |
| Organized By: Lucia Caporaso (U. Rome III), Brendan Hassett (Rice U.), James McKernan (MIT), Mircea Mustata (U. Michigan), Mihnea Popa (U. Illinois - Chicago) |
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| Parent Programs: |
| Algebraic Geometry |
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| Return to Workshop Description |
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Syzygies and Geometry
Friday January 30, 2009
02:00PM - 03:00PM
Speakers:
David Eisenbud
Abstract:
The graded betti numbers of a homogenous
ideal or graded module refine the information in the
Hilbert function or Euler characteristic. Another way
to look at the graded betti numbers is through Green's
notion of Koszul homology. Among the most interesting connections
of these invariants to geometry are Green's conjectures
(proven by Teixidor and Voisin in the generic case) about
canonical curves, and Farkas' use of Koszul homology to
distinguish other subvarieties of the moduli space of curves.
In this expository talk, I'll explain the basic definitions and facts about graded betti numbers,
and then outline some recent applications, such as measuring
the complexity of fibers of a linear projection, distinguishing
components of punctual Hilbert schemes, and describing the
cone of possible cohomology tables of vector bundles and
sheaves.
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