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Summer Graduate School

Toric Varieties July 29, 2019 - August 09, 2019
Parent Program: --
Location: National Center for Theoretical Sciences, Taipei
Organizers David Cox (Amherst College), Henry Schenck (Iowa State University)
Speaker(s)

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Description
Firstchoice cropped
This simplicial fan in 3-dimensional space

Toric varieties are algebraic varieties defined by combinatorial data, and there is a wonderful interplay between algebra, combinatorics and geometry involved in their study. Many of the key concepts of abstract algebraic geometry (for example, constructing a variety by gluing affine pieces) have very concrete interpretations in the toric case, making toric varieties an ideal tool for introducing students to abstruse concepts.

For eligibility and how to apply, see the Summer Graduate Schools homepage

Suggested Prerequisites:

  • Chapters 1,2,3,4,5,8 of "Ideals, Varieties and Algorithms" and Sections 1.0, 2.0, 3.0, 4.0 and 6.0 of "Toric Varieties" (Section 0 of these chapters is a background section that discusses algebraic geometry with no knowledge of toric varieties required).  An alternative to the Sections 0 would be my notes "Introduction to Algebraic Geometry", available at my web site https://dacox.people.amherst.edu/.
  • Chapters 1,2,3,4 of Ravi Vakil's excellent text "Foundation of Algebraic Geometry", freely available at math.stanford.edu/~vakil/216blog/FOAGjun1113public.pdf
  • Chapters 1 and 2 of Hartshorne's "Algebraic Geometry".

Due to the small number of students supported by MSRI, only one student per institution will be funded by MSRI.

Keywords and Mathematics Subject Classification (MSC)
Schedule, Notes/Handouts & Videos
Show Schedule, Notes/Handouts & Videos
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Jul 29, 2019
Monday
09:30 AM - 09:30 AM
  Affine toric varieties (Ch 1)
David Cox (Amherst College)
10:30 AM - 11:00 AM
  Coffee/Tea Break
11:00 AM - 12:00 PM
  Affine toric varieties (Ch 1)
David Cox (Amherst College)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 03:00 PM
  Begin problem session
03:00 PM - 03:15 PM
  Coffee/Tea Break
03:15 PM - 04:15 PM
  Continue problem session
04:15 PM - 05:20 PM
  Student presentations on problems
05:30 PM - 06:50 PM
  Dinner
Jul 30, 2019
Tuesday
09:30 AM - 09:30 AM
  Projective toric varieties (Ch 2)
Hal Schenck
10:30 AM - 11:00 AM
  Coffee/Tea Break
11:00 AM - 12:00 PM
  Projective toric varieties (Ch 2)
Hal Schenck
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 03:00 PM
  Begin problem session
03:00 PM - 03:15 PM
  Coffee/Tea Break
03:15 PM - 04:15 PM
  Continue problem session
04:15 PM - 05:20 PM
  Student presentations on problems
05:30 PM - 06:50 PM
  Dinner
Jul 31, 2019
Wednesday
09:30 AM - 09:30 AM
  Normal toric varieties (Ch 3)
David Cox (Amherst College)
10:30 AM - 11:00 AM
  Coffee/Tea Break
11:00 AM - 12:00 PM
  Normal toric varieties (Ch 3)
David Cox (Amherst College)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 03:00 PM
  Begin problem session
03:00 PM - 03:15 PM
  Coffee/Tea Break
03:15 PM - 04:15 PM
  Continue problem session
04:15 PM - 05:20 PM
  Student presentations on problems
05:30 PM - 06:50 PM
  Dinner
Aug 01, 2019
Thursday
09:30 AM - 09:30 AM
  Divisors on toric varieties (Ch 4)
Hal Schenck
10:30 AM - 11:00 AM
  Coffee/Tea Break
11:00 AM - 12:00 PM
  Divisors on toric varieties (Ch 4)
Hal Schenck
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 03:00 PM
  Begin problem session
03:00 PM - 03:15 PM
  Coffee/Tea Break
03:15 PM - 04:15 PM
  Continue problem session
04:15 PM - 05:20 PM
  Student presentations on problems
05:30 PM - 06:50 PM
  Dinner
07:00 PM - 08:00 PM
  Quotients in Algebraic Geometry
David Cox (Amherst College)
Aug 02, 2019
Friday
09:30 AM - 09:30 AM
  Homogeneous coordinates and quotient constructions (Ch 5)
David Cox (Amherst College)
10:30 AM - 11:00 AM
  Coffee/Tea Break
11:00 AM - 12:00 PM
  Homogeneous coordinates and quotient constructions (Ch 5)
David Cox (Amherst College)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 03:00 PM
  Begin problem session
03:00 PM - 03:15 PM
  Coffee/Tea Break
03:15 PM - 04:15 PM
  Continue problem session
04:15 PM - 05:20 PM
  Student presentations on problems
05:30 PM - 06:50 PM
  Dinner
Aug 05, 2019
Monday
09:30 AM - 09:30 AM
  Line bundles on toric varieties (Ch 6)
Hal Schenck
10:30 AM - 11:00 AM
  Coffee/Tea Break
11:00 AM - 12:00 PM
  Line bundles on toric varieties (Ch 6)
Hal Schenck
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 03:00 PM
  Begin problem session
03:00 PM - 03:15 PM
  Coffee/Tea Break
03:15 PM - 04:15 PM
  Continue problem session
04:15 PM - 05:20 PM
  Student presentations on problems
05:30 PM - 06:50 PM
  Dinner
07:00 PM - 08:00 PM
  Reflexive Sheaves and Differentials
David Cox (Amherst College)
Aug 06, 2019
Tuesday
09:30 AM - 09:30 AM
  Quasi-projective toric varieties and the canonical sheaf of a toric variety (Ch 7/8)
David Cox (Amherst College)
10:30 AM - 11:00 AM
  Coffee/Tea Break
11:00 AM - 12:00 PM
  Quasi-projective toric varieties and the canonical sheaf of a toric variety (Ch 7/8)
David Cox (Amherst College)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 03:00 PM
  Begin problem session
03:00 PM - 03:15 PM
  Coffee/Tea Break
03:15 PM - 04:15 PM
  Continue problem session
04:15 PM - 05:20 PM
  Student presentations on problems
05:30 PM - 06:50 PM
  Dinner
07:00 PM - 08:00 PM
  Sheaf Cohomology
Hal Schenck
Aug 07, 2019
Wednesday
09:30 AM - 09:30 AM
  Sheaf cohomology of toric varieties
Hal Schenck
10:30 AM - 11:00 AM
  Coffee/Tea Break
11:00 AM - 12:00 PM
  Sheaf cohomology of toric varieties
Hal Schenck
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 03:00 PM
  Begin problem session
03:00 PM - 03:15 PM
  Coffee/Tea Break
03:15 PM - 04:15 PM
  Continue problem session
04:15 PM - 05:20 PM
  Student presentations on problems
05:30 PM - 06:50 PM
  Dinner
Aug 08, 2019
Thursday
09:30 AM - 09:30 AM
  Toric surfaces (Ch 10)
David Cox (Amherst College)
10:30 AM - 11:00 AM
  Coffee/Tea Break
11:00 AM - 12:00 PM
  Toric surfaces (Ch 10)
David Cox (Amherst College)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 03:00 PM
  Begin problem session
03:00 PM - 03:15 PM
  Coffee/Tea Break
03:15 PM - 04:15 PM
  Continue problem session
04:15 PM - 05:20 PM
  Student presentations on problems
05:30 PM - 06:50 PM
  Dinner
07:00 PM - 08:00 PM
  Singular and Equivariant Cohomology
Hal Schenck
Aug 09, 2019
Friday
09:30 AM - 09:30 AM
  Singular and equivariant cohomology of toric varieties and Riemann-Roch (Ch 12/13)
Hal Schenck
10:30 AM - 11:00 AM
  Coffee/Tea Break
11:00 AM - 12:00 PM
  Singular and equivariant cohomology of toric varieties and Riemann-Roch (Ch 12/13)
Hal Schenck
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 02:30 PM
  Introduction to Chapters 14 and 15 - Secondary Fan
David Cox (Amherst College)
02:30 PM - 03:30 PM
  Lecture
Kuei-Nuan Lin (Pennsylvania State University)
03:30 PM - 04:00 PM
  Farewell coffee/tea
04:00 PM - 05:00 PM
  Lecture
Jen-Chieh Hsiao (Purdue University)