Universal cohomological expressions for singularities in families of genus 0 stable maps

TL;DR

This paper derives universal cohomological formulas for the classes of singularities in families of genus 0 stable maps, applicable under certain versality conditions, advancing the understanding of their geometric structure.

Contribution

It provides universal cohomological expressions for singularity loci in families of genus 0 stable maps, generalizing previous specific cases.

Findings

Universal formulas for singularity classes in genus 0 stable maps

Applicable to any family satisfying versality and singularity conditions

Enhances understanding of the geometry of curve-to-curve map families

Abstract

We consider families of curve-to-curve maps that have no singularities except those of genus 0 stable maps and that satisfy a versality condition at each singularity. We provide a universal expression for the cohomology class Poincar\'e dual to the locus of any given singularity. Our expressions hold for any family of curve-to-curve maps satisfying the above properties.