Introduction to toric varieties
Toric geometry has been playing an increasingly important role in mathematics in recent years.
It is on the edge of algebraic geometry (the study of the geometry of zero locus of polynomials) and combinatorics, allowing a beautiful interplay among them.
The main object of this series of lectures are toric varieties. I will present a detailed introduction to affine, projective and
abstract toric varieties from the point of view of the torus action, geometry of cones and properties of polytopes.
In simplest terms, a toric variety is the closure of the image of a monomial map.
Tools from combinatorics make toric varieties one of the most well-understood classes of algebraic varieties.
On the other hand, deep theorems in algebraic geometry allow to deduce highly nontrivial facts about lattice polytopes.
Although my lectures will be only at an introductory level, I hope to provide connections to many branches of pure and applied mathematics.
In particular, I hope that any student following them will have tools necessary to further study (and recognize in his/her research) toric varieties.
During the lectures I will be giving easy exercises and, for interested students, open problems.
Place: Research Bldg. No.2, ROOM 478 (€QΩSVWΊ)
See here (building "34")
Schedule: Every Thursday, from 14:00 to 15:00
- October, 6
- October, 13
- October, 20
- October, 27
- November, 10
- November, 17
- November, 24
- December, 1
- December, 15, from 14:00 to 15:00 and from 15:30 to 16:30
scanned lecture note (uploaded at Dec. 19)
the final proceeding (uploaded at Dec. 19).