Organizer: Hechen Hu
Toric varieties are algebraic varieties admitting a dense open subset isomorphic to a torus such that the translation action of the torus on itself extends to an action of the whole variety. Although they are quite special (e.g. such varieties are necessarily rational), the theory of toric varieties have many applications in areas such as combinatorics and symplectic geometry. Moreover, the torus action enables these varieties to be described via the combinatorial data of fans in a real vector space. The purpose of this seminar is to go over the basic theory of toric varieties, covering how the various algebro-geometric concepts, such as divisors and sheaf cohomology, can be described combinatorially, as well as some topological notions like their fundamental groups and Euler characteristics. Later in the semester we will also explore related topics (e.g. continued fractions) depending on participant interests.
If you’d like to sign up for a talk, suggest a topic, or just to be added to the mailing list, please email me at [email protected].
Math 528, Wednesday 5pm-6:30pm
[CLS]: Toric Varieties (Cox, Little, Schenck)
[F]: Introduction to Toric Varieties (Fulton)
[O]: Convex Bodies and Algebraic Geometry (Oda)
[ELST]: Arithmetic Toric Varieties (Elizondo, Lima-Filho, Sottile, Teitler)