Summer 2022 Topic:
Summer 2022 Topic:
Toric Varieties
Toric Varieties
We will study toric varieties and the role they play in mirror symmetry. We begin with an overview of the techniques used to examine the geometry of toric varieties, including computations of the class group and the Picard group, as well as the intersection pairing on homology/cohomology. Since the geometry of toric varieties is particularly nice, the mirror map is particularly easy to construct, and we will finish with an examination of Baytrev's mirror symmetry for toric varieties.
Resources:
Fulton, William. Introduction to Toric Varieties. No. 131. Princeton university press, 1993.
Cox, David A., John B. Little, and Henry K. Schenck. Toric varieties. Vol. 124. American Mathematical Soc., 2011.
Cox, David A., and Sheldon Katz. Mirror symmetry and algebraic geometry. Vol. 68. Providence, RI: American Mathematical Society, 1999.
Past Talks:
Introduction to Toric Varieties (Daniel Halmrast), August 23, 2022. PDF
Introduction to Toric Varieties II (Chris Dare), August 30 / Sept 7, 2022. PDF
Gauged Linear Sigma Models, GW Invariants & Mirror Theorem for Toric Varieties (Danning Lu), August 30, 2022. PDF
Introduction to Toric Varieties III (Daniel Halmrast, Chris Dare), September 13, 2022. PDF