A complex surface of general type with p_g=0, K^2=3 and H_1=Z/2Z

TL;DR

This paper constructs a new minimal complex surface of general type with specific invariants, including p_g=0, K^2=3, and fundamental group Z/2Z, using advanced surgical and smoothing techniques.

Contribution

It introduces a novel construction of a non-simply connected surface of general type with these invariants, expanding the known examples in the field.

Findings

Successfully constructed a surface with p_g=0, K^2=3, H_1=Z/2Z

Applied rational blow-down surgery and Q-Gorenstein smoothing

Extended the class of known surfaces with these invariants

Abstract

This paper is an addendum to [4], in which the authors constructed a simply connected minimal complex surface of general type with p_g=0 and K^2=3. In this paper we construct a new non-simply connected minimal surface of general type with p_g=0, K^2=3 and H_1=Z/2Z using a rational blow-down surgery and Q-Gorenstein smoothing theory.