KNU Mathematics Intensitve Lecture Series

Introduction to Toric Geometry

given by

Prof. Yunhyung Cho (Sungkyunkwan University)

October – December, 2023

Abstract

Toric varieties are algebraic varieties defined by certain combinatorial data and there are beautiful correspondences between algebraic/topological/geometric theories and combinatorial theories. Moreover, the theory of toric varieties can be widely generalized via toric degenerations. In this series of lectures, I will give an introduction to those theories. If time permits, I will also introduce a certain relationship between toric varieties in terms of the theory of cluster algebras.

Lectures

Part I -- Definition of Toric varieties and Many Examples

Lecture note is here.

Introduction to algebraic varieties (Atiyah-MacDonald), October 16(Mon), 16:00 – 17:30
Affine toric varieties (Cox Chap. 1), October 17(Tue), 13:00 – 14:30
Projective toric varieties (Cox Chap. 2), October 23(Mon), 16:00 – 17:30
Normal toric varieties (Cox Chap. 3), October 24(Tue), 13:00 – 14:30

Part II -- Geometry and Topology of Toric Varieties

Lecture note is here.

Introduction to Divisors, December 11(Mon), 16:00 – 17:30
Divisors on Toric varieties (Cox Chap. 4), December 12(Tue), 14:00 – 15:30
Sheaves on Toric varieties (Cox Chap. 5), December 18(Mon), 16:00 – 17:30
Ample divisors and Fano toric varieties (Cox Chap. 6, 8), December 19(Tue), 14:00 – 15:30
Topology of Toric varieties (Cox Chap. 12), Deceber 26(Tue), 16:30 – 18:00
Examples: Toric surfaces (Cox Chap. 11), December 27(Wed), 13:30 – 15:00

Venue

#102, College of Natural Sciences, Kyungpook National University, Daegu, Korea

Participants

Byunghee An (KNU)
Hyunseung Choi (KNU)
Jaewoo Jeong (IBS-CCG)
Boran Kim (KNU)
Junho Kim (CNBU)
Hayeon Kim (Yonsei University)
Hyunbin Kim (Yonsei University)
Minhoon Kim (KNU)
Minseong Kwon (KAIST)
Eunjeong Lee (CBNU)
Jeehoon Park (KNU)
Semin Yoo (KIAS)