We prove a localization formula for the moduli space of stable relative maps. As an application, we prove that all codimension i tautological classes on the moduli space of stable pointed curves… Expand

We consider the question: “How bad can the deformation space of an object be?” The answer seems to be: “Unless there is some a priori reason otherwise, the deformation space may be as bad as… Expand

Abstract:In [CH3], Caporaso and Harris derive recursive formulas counting nodal plane curves of degree d and geometric genus g in the plane (through the appropriate number of fixed general points).… Expand

Hurwitz numbers, which count certain covers of the projective line (or, equivalently, factorizations of permutations into transpositions), have been extensively studied for over a century. The… Expand

We describe a geometric Littlewood-Richardson rule, interpreted as deforming the intersection of two Schubert varieties into the union of Schubert varieties. There are no restrictions on the base… Expand

We consider the "limiting behavior" of *discriminants*, by which we mean informally the locus in some parameter space of some type of object where the objects have certain singularities. We focus on… Expand

In this section, we briefly describe the objects under consideration for the sake of non-experts. A more detailed informal exposition of these well-known ideas is given in [PV]. When studying Riemann… Expand

A BSTRACT . We describe a Schubert induction theorem, a tool for analyzing intersections on a Grassmannian over an arbitrary base ring. The key ingredient in the proof is the Geometric… Expand