Building the Fan of a Toric Variety (Professor Reginald Anderson, Claremont McKenna College)

Title: Building the Fan of a Toric Variety

Speaker: Reginald Anderson, Department of Mathematical Sciences, Claremont McKenna College

Abstract: Roughly speaking, algebraic geometry studies the zero sets of polynomials, which lead to objects called varieties. Since the zero sets of polynomials do not always pass the vertical line test, we enlist other methods to study them besides considering the graph of a function. This is analogous to the use of implicit differentiation in calculus. One such method uses line bundles to understand a variety in terms of its algebraic subspaces. Since the zero sets of polynomials can become complicated in multiple variables over the complex numbers, one simplifying assumption we can impose is that the variety contain a dense, open algebraic torus. This leads to the notion of a toric variety. I will describe the fan of a toric variety for the complex projective line, and mention some recent results concerning toric varieties.