Real representatives of equisingular strata of simple quartic surfaces

TL;DR

This paper introduces an algorithm to identify real representatives in equisingular strata of K3 surfaces, applies it to spatial quartics, and discovers new examples of real strata lacking real representatives, also providing a new proof for a known case.

Contribution

The paper presents a novel algorithm for detecting real representatives in equisingular strata and applies it to spatial quartics, revealing new phenomena in real algebraic geometry.

Findings

Found two new real strata without real representatives.

Provided a new proof for the unique known example of plane sextics.

Developed an effective algorithm for analyzing real representatives in K3 surface models.

Abstract

We develop an algorithm detecting real representatives in equisingular strata of projective models of $K3$-surfaces. We apply this algorithm to spatial quartics and find two new examples of real strata without real representatives. As a by-product, we also give a new proof for the only previously known example of plane sextics.