Combinatorics of lattice polytopes and MMP

Abstract: The Minimal Model Program (MMP) was born in 80-ties from attempts to extend classical results on the birational classification of algebraic surfaces to algebraic varieties of dimension >2. The problem of birational classification of higher dimensional algebraic varieties is so difficult that its complete solution is not even expected. However, a significant progress in understanding this problem can be achieved if one restricts attention to some special and simultaneously sufficiently rich class of algebraic varieties under consideration.

The talk suggests to look at the class of algebraic varieties that are birational to non-degenerate hypersurfaces Z in an algebraic torus T. It turns out that this class is sufficiently rich to illustrate many important ideas of MMP using combinatorial properties of the Newton polytope P of the defining equation of Z. The purpose of the talk is to explain the interplay between the combinatorics of lattice polytopes and MMP which benefits from studing its “combinatorial shadows”.

computational geometrydiscrete mathematicscommutative algebracombinatorics

Audience: researchers in the topic

Copenhagen-Jerusalem Combinatorics Seminar

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The password for the zoom room is 123456