Working Seminar on Algebraic Cycles and Toric Varieties

2025-26

This year's working seminar will be on Algebraic Cycles and Toric Varieties. We will spend the first half of the semester learning about algebraic cycles, then introduce toric varieties from the foundations, with the aim of learning about algebraic cycles in the friendly example of toric varieties by the end of the semester.

Schedule: Wednesdays, 3:30pm in MATH-103

Literature:For the algebraic cycles part:

Main reference: Voisin, Hodge theory and Complex Algebraic Geometry, Volume 2, Chapter 9
Fulton, Intersection theory
Eisenbud and Harris, 3264 and all that
Ricolfi, An invitation to modern enumerative geometry

For the toric varieties part:

Main reference: Fulton, Introduction to Toric Varieties
Cox-Little-Schenk's Toric Varieties
Oda's Convex bodies and algebraic geometry

Tentative plan:

Day	Speaker	Title	References
24 September	Nicola	Rational equivalences and functoriality	Voisin 9.1.1 and 9.1.2
1 October	Naoki	Rational equivalences and functoriality part II	Voisin 9.1.1 and 9.1.2
8 October	Yushu	Examples: vector bundles, P^n bundles, and blow-ups	Voisin 9.1.3 and 9.3
15 October 4pm	Zifang	Definition of intersection product, correspondences	Voisin 9.2.1 and 9.2.2
22 October	Yuxiao	Cycle class map, compatibility with cup product, Chow's moving lemma	Voisin 9.2.3 and 9.2.4 (first half)
29 October	tba	Consolidation week	-
5 November	Nick	Cones and affine toric varieties	Fulton 1.1, 1.2, 1.3, 3.1
12 November	Adil	Fans and abstract toric varieties	Fulton 2.1, 1.4, 2.4, 2.5
19 November	tba	Line bundles on toric varieties	Fulton 3.3, 3.4
26 November	tba	Cohomology of line bundles on toric varieties	Fulton 3.5, 4.3, 4.4
3 December	tba	Chow groups and intersection theory for toric varieties	Fulton 5.1, 5.2