Extremal Laurent Polynomials and Fano Manifolds
Talk by Prof. Dr. Alessio Corti
Speaker invited by: Prof. Dr. Andrew Kresch
Date: 30.05.11 Time: 13.15 - 14.45 Room: Y27H25
A Laurent polynomial is extremal if the Picard-Fuchs system has smallest possible ramification. I explain how extremal Laurent polynomials (ELP) mirror the quantum cohomology of Fano manifolds. I describe a class of ELP called Minkowski polynomials, and I show that the list of Minkowski polynomials in three variables allows one to recover the classification of Fano 3-folds of Fano, Iskovskikh and Mori-Mukai. I discuss a project to list Minkowski polynomials in four variables and implications for the classification of Fano 4-folds. This is experimental work in progress with Tom Coates, Sergei Galkin, Vasily Golyshev and Al Kasprzyk