On the Pontrjagin-Viro form

TL;DR

This paper introduces the Pontrjagin-Viro form, a new invariant for algebraic surfaces, explores its connections to existing forms, and computes it for specific real Enriques surfaces.

Contribution

It presents the Pontrjagin-Viro form as a novel invariant and extends the understanding of algebraic surface invariants by relating it to known forms and calculating it explicitly.

Findings

The Pontrjagin-Viro form is related to Rokhlin-Guillou-Marin forms.

It generalizes Mikhalkin's complex separation.

The form is explicitly computed for real Enriques surfaces.

Abstract

A new invariant, the Pontrjagin-Viro form, of algebraic surfaces is introduced and studied. It is related to various Rokhlin-Guillou-Marin forms and generalizes Mikhalkin's complex separation. The form is calculated for all real Enriques surfaces for which it is well defined.