Non-planar degenerations and related fundamental groups

TL;DR

This paper explores algebraic surfaces with non-planar degenerations, focusing on their Galois covers and fundamental groups, revealing their distinct positions in the moduli space.

Contribution

It introduces the study of non-planar degenerations like the tetrahedron and double tetrahedron and analyzes their fundamental groups and moduli space components.

Findings

Fundamental groups differ for tetrahedron and double tetrahedron.

These surfaces occupy different components in the moduli space.

Preliminary investigation suggests diverse degenerations impact moduli classification.

Abstract

We present a preliminary investigation of algebraic surfaces that have non-planar degenerations, along with their Galois covers and fundamental groups. Specifically, we investigate the tetrahedron and the double tetrahedron. The resulting fundamental groups indicate that the tetrahedron and the double tetrahedron are in different components of the moduli space of algebraic surfaces.