A simply connected surface of general type with $p_g=1$, $q=0$, and $K^2=8$

TL;DR

This paper constructs a new family of simply connected minimal complex surfaces with specific invariants using $ ext{Q}$-Gorenstein smoothing, advancing the understanding of surfaces of general type.

Contribution

It introduces a novel construction method for simply connected surfaces of general type with $p_g=1$, $q=0$, and $K^2=8$ via $ ext{Q}$-Gorenstein smoothing.

Findings

New family of surfaces constructed

Surfaces have $p_g=1$, $q=0$, $K^2=8$

Construction method broadens understanding of complex surfaces

Abstract

We construct a new family of simply connected minimal complex surfaces with $p_g=1$, $q=0$, and $K^2=8$ using a $\mathbb{Q}$-Gorenstein smoothing theory.