Burniat-type surfaces and a new family of surfaces with p_g = 0, K^2 = 3

TL;DR

This paper generalizes Burniat's classical construction to produce new surfaces of general type with p_g=0, K^2=3, and a novel fundamental group of order 16, advancing the classification of such surfaces.

Contribution

It introduces a new family of surfaces with specific invariants and a unique fundamental group, expanding the known landscape of surfaces with p_g=0.

Findings

Constructed surfaces with K^2=3 and p_g=0

Discovered a new fundamental group of order 16

Contributed to the classification of surfaces of general type

Abstract

In this paper, one of a series devoted to the classification, the moduli spaces and the discovery of new surfaces of general type with geometric genus p_g= 0, we generalize a classical construction method due to Burniat (and revisited by Inoue), constructing surfaces with K^2 = 3 and a with a new fundamental group of order 16.