Algebraic Geometry Seminar
We will review the role of Segre classes in intersection theory, and use them to define a 'Segre zeta function' for homogeneous ideals of polynomial rings. It can be shown that this function is rational, with poles determined by some of the generators. We will present an explicit formula computing this function for schemes that are 'monomial' with respect to a collection of possibly singular hypersurfaces meeting along complete intersections. The formula is expressed as a formal integral over a Newton polytope associated with the scheme.