Recursive formulas for Welschinger invariants of the projective plane

TL;DR

This paper introduces a combinatorial approach using marked floor diagrams to compute Welschinger invariants of the real projective plane, providing a recursive formula applicable to various point configurations.

Contribution

It establishes a Caporaso-Harris type recursive formula for Welschinger invariants based on combinatorial enumeration of enriched graphs.

Findings

Derived a recursive formula for Welschinger invariants

Enabled computation for configurations with multiple conjugated points

Provided a combinatorial framework for invariants calculation

Abstract

Welschinger invariants of the real projective plane can be computed via the enumeration of enriched graphs, called marked floor diagrams. By a purely combinatorial study of these objects, we prove a Caporaso-Harris type formula which allows one to compute Welschinger invariants for configurations of points with any number of complex conjugated points.