A simply connected surface of general type with p_g=0 and K^2=4

TL;DR

This paper constructs a new example of a simply connected minimal complex surface of general type with specific invariants p_g=0 and K^2=4, using advanced surgical and smoothing techniques.

Contribution

It introduces a novel construction method for such surfaces, expanding the known examples in algebraic geometry.

Findings

Successfully constructed a simply connected surface with p_g=0 and K^2=4

Applied rational blow-down surgery and Q-Gorenstein smoothing techniques

Provides new insights into the classification of complex surfaces

Abstract

As the sequel to [5, 7], we construct a simply connected minimal complex surface of general type with p_g = 0 and K^2 = 4 by using a rational blow-down surgery and Q-Gorenstein smoothing theory.