# Singular Welschinger invariants

## TL;DR

This paper introduces a new invariant method for counting real plane curve singularities with nodes and cusps by assigning Welschinger signs, providing a local perspective on real rational curve enumeration.

## Contribution

It proposes a novel invariant approach to count real deformations of plane curve singularities using Welschinger signs, extending the concept locally.

## Key findings

- Defines a new invariant for real curve singularities.
- Connects local invariants to global Welschinger invariants.
- Provides a method to count real deformations with signs.

## Abstract

We suggest an invariant way to enumerate nodal and nodal-cuspidal real deformations of real plane curve singularities. The key idea is to assign Welschinger signs to the counted deformations. Our invariants can be viewed as a local version of Welschinger invariants enumerating real plane rational curves.