Classification of simple quartics up to equisingular deformation

TL;DR

This paper classifies simple quartic surfaces with simple singularities based on their equisingular deformations, providing a comprehensive understanding of their deformation types.

Contribution

It offers the first complete classification of non-special simple quartic surfaces under equisingular deformations, advancing the understanding of their geometric properties.

Findings

Complete classification of non-special simple quartic surfaces

Identification of deformation types for these surfaces

Enhanced understanding of their singularity structures

Abstract

We study complex spatial quartic surfaces with simple singularities up to equisingular deformations; as a first step, give a complete equisingular deformation classification of the so-called non-special simple quartic surfaces.