A simply connected surface of general type with p_g=0 and K^2=3

TL;DR

This paper constructs new examples of simply connected complex surfaces of general type with specific invariants, using advanced surgical and smoothing techniques, expanding the known landscape of such surfaces.

Contribution

It introduces novel constructions of simply connected surfaces with p_g=0, K^2=3, and a symplectic 4-manifold with b_2^+=1, K^2=4, employing rational blow-down and Q-Gorenstein smoothing.

Findings

Constructed a simply connected minimal complex surface with p_g=0, K^2=3.

Built a new simply connected symplectic 4-manifold with b_2^+=1, K^2=4.

Abstract

Motivated by a recent result of Y. Lee and the second author[7], we construct a simply connected minimal complex surface of general type with p_g=0 and K^2=3 using a rational blow-down surgery and Q-Gorenstein smoothing theory. In a similar fashion, we also construct a new simply connected symplectic 4-manifold with b_2^+=1 and K^2=4.