## MATHEMATICS 595TV, TORIC VARIETIES, SPRING 2023

**Instructor:** Sheldon Katz

**Email/Phone:** katzs AT illinois.edu/217-265-6258 (email is usually quicker than phone)

** Office and Hours:** To be announced, 301 Altgeld Hall, or by appointment

**Class Time and location:** TuTh 12:30-1:45, 113 Davenport Hall.

**Text:** Introduction to Toric Varieties, W. Fulton, Annals of Math Studies 131, Princeton University Press, Princeton NJ 1993. ([F])

**Supplementary Texts:** Mirror Symmetry and Algebraic Geometry, D.A. Cox and S. Katz (Chapter 3 only) ([CK]), and Toric Varieties, D.A. Cox , J. Little, and H. Schenck ([CLS]).

**Reserves:** Hardcopy of all of the above texts are on reserve at the Mathematics Library. Electronic copies of [F] and [CK] are available, but not of [CLS]. However, here is a preliminary version of [CLS], posted with permission of the authors.

**Course Syllabus** is here.

**Weekly class plans**
- Week 1 (Jan 17 and 19). Read [F] Ch. 1. See [CLS] Ch. 1 for more detail. Start homework 1.
- Week 2 (Jan 24 and 26). Read [F] Chapters 1.3,1.4,2.1. There will be a problem session in class on January 26.
- Week 3 (Jan 31 and Feb 2). Read [F] Chapters 2.2-2.5. See [CLS] Chapters 3.2, 3.4 for another perspective and more detail on some of these topics.
- Week 4 (Feb 7 and 9). Read [F] Chapters 2.5-2.6,3.1. There will be a problem session in class on February 9.
- Week 5 (Feb 14 and 16). Read [F] Chapters 3.1, 3.3, 3.4. See [CLS] Ch. 4 for more detail.
- Week 6 (Feb 21 and 23). Read [F] Chapter 3.4 and [CK] Chapter 3.1-3.2. The material from [CK] Section 3.2.1 and 3.2.2 will be supplemented with selected material from [CLS] Chapter 2. There will be a problem session in class on February 23.
- Week 7 (Feb 28 and March 2). Read [CK] Section 3.2.3-3.2.4 and [CLS] Chapter 5. Then read [CK] 3.2.1-3.2.2.
- Week 8 (March 7 and 9). Read [CLS] Chapter 5 and [CK] 3.2.1-3.2.2.

**Homeworks:** [F]=Fulton; [CLS]=Cox-Little=Schenck
- Homework 1, for discussion during the Thursday, January 26 Problem Session.
- Homework 2, for discussion during the Thursday, February 9 Problem Session.
- Homework 3, for discussion during the Thursday, February 23 Problem Session.

**Updates and announcements**
- There will not be a problem session during the last week of class
- The last day of class will be Thursday, March 9.

**Seminars and other activities of interest**
- Graduate Algebraic Geometry and Commutative Algebra Seminar,
Wednesdays at 3pm in AH 341. Talks will be posted on the department's seminar calendar