Toric Varieties Fan Club

This is the page for the Spring 2021 Toric Varieties Fan Club (Reading Group), which is open to all UW Math grad students, but will require a certain amount of participation and work to receive course credit (details below).

Resources

We plan to read Cox, Little, and Schenck's Toric Varieties, which can be downloaded here: [1].

Meeting Schedule

14 weeks total, starting on January 25, adjusting throughout the semester as necessary.

Meetings will be on Mondays and Wednesdays at 1-2:30pm, where the first hour is devoted to reviewing the assigned reading (about 10 pages), led by a designated speaker, and the half-hour is used to collaborate on exercises. Meetings will be held virtually using this link: [2].

Optimistic Reading Schedule:

Week 1

Monday, January 25: Ch. 1.0 Affine Varieties Background  (Speaker: Ola Sobieska)

Wednesday, January 27: Ch. 1.1 Introduction to Affine Toric Varieties  (Speaker: Ola Sobieska)

Week 2

Monday, February 1: Ch. 1.2 Cones and Affine Toric Varieties   (Speaker: Ivan Aidun)

Wednesday, February 3: Ch. 1.3 Properties of Affine Toric Varieties  (Speaker: Ola Sobieska)

Week 3

Monday, February 8: Ch. 2.1 Lattice Points and Projective Toric Varieties   (Speaker: Zinan Wang)

Wednesday, February 10: Ch. 2.2 Lattice Points and Polytopes  (Speaker: Maya Banks)

Week 4

Monday, February 15: Ch. 2.3 Polytopes and Projective Toric Varieties   (Speaker: Will Hardt)

Wednesday, February 17: Ch. 2.4 Properties of Projective Toric Varieties  (Speaker: TBD)

Week 5

Monday, February 22: Catch-up/Review Day

Wednesday, February 24: Ch. 3.1 Fans and Normal Toric Varieties  (Speaker: TBD)

Week 6

Monday, March 1: Ch. 3.2 The Orbit-Cone Correspondence (Speaker: TBD)

Wednesday, March 3: Ch. 3.3 Toric Morphisms  (Speaker: TBD)

Week 7

Monday, March 8: Ch. 3.4 Complete and Proper (Speaker: TBD)

Wednesday, March 10: Catch-up/Review Day

Week 8

Monday, March 15: Ch. 4.0 Valuations, Divisors, and Sheaves Background (Speaker: TBD)

Wednesday, March 17: Ch. 4.1 Weil Divisors on Toric Varieties (Speaker: TBD)

Week 9

Monday, March 22: Ch. 4.2 Cartier Divisors on Toric Varieties (Speaker: TBD)

Wednesday, March 24: Ch. 4.3 The Sheaf of a Torus-Invariant Divisor (Speaker: TBD)

Week 10

Monday, March 29: Ch. 5.0 Quotients in Algebraic Geometry Background (Speaker: TBD)

Wednesday, March 31: Ch. 5.1 Quotient Constructions of Toric Varieties (Speaker: TBD)

Week 11

Monday, April 5: Ch. 5.2 The Total Coordinate Ring (Speaker: TBD)

Wednesday, April 7: Ch. 5.3 Sheaves on Toric Varieties (Speaker: TBD)

Week 12

Monday, April 12: Ch. 5.4 Homogenization and Polytopes (Speaker: TBD)

Wednesday, April 14: Ch. 6.0 Sheaves and Line Bundles Background (Speaker: TBD)

Week 13

Monday, April 19: Ch. 6.1 Ample and Basepoint Free Divisors on Complete Toric Varieties (Speaker: TBD)

Wednesday, April 21: Ch. 6.2 Polytopes and Projective Toric Varieties (Speaker: TBD)

Week 14

Monday, April 26: Ch. 6.3 The Nef and Mori Cones (Speaker: TBD)

Wednesday, April 28: Ch. 6.4 The Simplicial Case (Speaker: TBD)

General Meeting Structure

This reading group will be structured as follows. Every meeting will have an assigned speaker, who will usually be one of the reading group participants, but could at times be a professor or other guest speaker. It will be expected that everyone attending will read the assigned sections prior to the meeting. The speaker is expected to additionally work out some examples prior and will be responsible for lecturing on the reading material and guiding the group discussion during the meeting. The schedule will be adjusted throughout the semester. Daniel Erman will be our faculty advisor, and in order to receive credit (up to 3 credits), participants will be expected to attend all meetings, be the speaker twice, and do several exercises. We may also use Macaulay2 during the exercise portions to get comfortable both computing examples by hand and by using a computer.

If you are interested in joining this reading group or have any questions, please contact Caitlyn Booms at cbooms@wisc.edu or Aleksandra (Ola) Sobieska at asobieska@wisc.edu by January 24, 2021.