On fake ES-irreducibile components of certain strata of smooth plane sextics

TL;DR

This paper introduces the concept of fake ES-irreducible components in certain strata of smooth plane sextics, providing the first examples and classifying automorphism groups with limited order automorphisms.

Contribution

It constructs the first examples of fake ES-irreducible components and classifies automorphism groups of smooth plane sextics with automorphisms of order at most 3.

Findings

First examples of fake ES-irreducible components

Classification of automorphism groups with automorphisms of order ≤ 3

Identification of specific strata of smooth plane sextics

Abstract

We construct the first examples of what we call fake ES-irreducible components; Definition 2.8. In our way to do so, we classify the automorphism groups of smooth plane sextics that only have automorphisms of order 3 or less; Theorems 2.1, 2.4 and 2.5, Corollaries 2.9 and 2.11.