Applications of Equivariant Cohomology to Enumerative Geometry

Abstract

We show how equivariant cohomology can be applied to enumerative geometry in three different settings: orbits of plane curves, strata of points on a line, and effective divisors on the moduli space of curves. We first give a brief introduction to equivariant cohomology. Then, we include three different applications that are essentially unchanged from their published versions and contain joint work with Mitchell Lee, Anand Patel, and Hunter Spink. We conclude with a short section with unpublished observations and conjectures stemming from a concrete connection between counting singularities and equivariant cohomology.