An obstruction to smoothing stable maps

TL;DR

This paper introduces a new obstruction to smoothing stable maps in smooth projective varieties, extending previous obstructions by analyzing rational functions on ghost components with specific poles and residues.

Contribution

It generalizes known obstructions by identifying a new type based on rational functions with prescribed poles on ghost components.

Findings

Identifies a new obstruction to smoothing stable maps.

Extends the understanding of obstructions beyond previous known cases.

Provides a framework for analyzing rational functions on ghost components.

Abstract

We describe an obstruction to smoothing stable maps in smooth projective varieties, which generalizes some previously known obstructions. Our obstruction comes from the non-existence of certain rational functions on the ghost components, with prescribed simple poles and residues.