Explicit Birational Geometry

Florin Ambro

Institute of Mathematics "Simion Stoilow"

of the Romanian Academy

Florin Ambro, Senior Researcher II at the Institute of Mathematics "Simion Stoilow" of the Romanian Academy.

Research Interests：

Algebraic Geometry. Classification theory, singularities.

Personal Website:

http://imar.ro/~fambro/

1

Time

Wed.& Fri., 9:50 - 11:25 am,

April 2-June 27, 2025

(excluding April 4, April 30 and May 2);

Tues., 9:50-11:25 am, April 29, 2025

2

Venue

C548, Shuangqing Complex Building A

Description

Toric varieties are geometric objects defined combinatorially, much like CW complexes in topology. They can be used to study geometrically combinatorial objects like semigroups, cones, polytopes or simplicial complexes. In Algebraic Geometry, toric varieties are a rich source of examples, a good testing ground for gaining intuition for open problems.

This course tours several topics of birational geometry, in the special case of toric varieties. The goal is to construct many explicit examples, of log structures, singularities, polarized varieties, and varieties of K-pure type (Fano, Calabi-Yau, canonically polarized).

We assume basic knowledge of Birational Geometry and Toric Varieties (for example Caucher Birkar's introductory course).