Seminar in Real and Complex Geometry

Thursday, December 12, 2024, 16:15-17:45, online via zoom




Victor Batyrev
(Universität Tübingen)

On birational minimal models of non-degenerate surfaces in 3-dimensional algebraic tori


Abstract
             
According to the classical birational classification of surfaces, every algebraic surface X of non-negative Kodaira dimension is birational to a unique smooth projective algebraic surface S which is called birational minimal model of X. We explicitly show this statement in case of non-degenerate affine surfaces X given as zero loci of Laurent polynomials F in 3-dimensional affine algebraic tori. The purpose of the talk is to give an explicit construction of the minimal birational model S of X and to explain combinatorial formulas for computing its main topological invariants using the 3-dimensional Newton polytope P of F.