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Toric Varieties (National Center for Theoretical Sciences, Taipei, Taiwan) July 29, 2019 - August 09, 2019
Parent Program: -- National Center for Theoretical Sciences, Taipei, Taiwan
Organizers David Cox (Amherst College), Henry Schenck (Auburn University)
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Description
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)
Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification
Schedule, Notes/Handouts & Videos
Show Schedule, Notes/Handouts & Videos
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) Henry Schenck (Auburn University) 10:30 AM - 11:00 AM Coffee/Tea Break 11:00 AM - 12:00 PM Projective toric varieties (Ch 2) Henry Schenck (Auburn University) 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) Henry Schenck (Auburn University) 10:30 AM - 11:00 AM Coffee/Tea Break 11:00 AM - 12:00 PM Divisors on toric varieties (Ch 4) Henry Schenck (Auburn University) 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) Henry Schenck (Auburn University) 10:30 AM - 11:00 AM Coffee/Tea Break 11:00 AM - 12:00 PM Line bundles on toric varieties (Ch 6) Henry Schenck (Auburn University) 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 Henry Schenck (Auburn University)
Aug 07, 2019
Wednesday
 09:30 AM - 09:30 AM Sheaf cohomology of toric varieties Henry Schenck (Auburn University) 10:30 AM - 11:00 AM Coffee/Tea Break 11:00 AM - 12:00 PM Sheaf cohomology of toric varieties Henry Schenck (Auburn University) 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 01:00 PM - 02:30 PM Intro to chapters 14 & 15 David Cox (Amherst College) 02:30 PM - 03:30 PM Kuei-Nuan Lin Lecture Kuei-Nuan Lin (Pennsylvania State University) 03:30 PM - 04:30 PM Jen-Chieh Hsiao Lecture Jen-Chieh Hsiao (Purdue University)
Aug 09, 2019
Friday
 08:00 AM - 06:00 PM Canceled due to Typhoon.