Date/Time
Date(s) - 19/11/2024
11:30 am - 12:30 pm

Location: Hamilton Hall, Room 312

Speaker: Alexandre Zotine

Title: Computing Higher Direct Images of Toric Morphisms

Abstract: Higher direct images allow one to package a large number of invariants into one algebraic object. Such invariants include the dimensions of each variety, their degrees, and more relative notions like the dimensions of the fibre over a point, among others. In practice, it is difficult to compute these as they are defined using a derived functor. By specializing to toric varieties, we obtain a combinatorial framework for computing these higher invariants. This translates most of the complicated geometry we need to worry about into algebra and combinatorics, and I will try to emphasize this accessibility during the talk.

 We will discuss an algorithm I implemented in Macaulay2 for computing the higher direct images of any line bundle for surjective toric morphisms. This is joint work with Mike Roth and Greg Smith.