Simply connected surfaces of general type in positive characteristic via deformation theory

TL;DR

This paper constructs algebraically simply connected surfaces of general type in positive characteristic using Q-Gorenstein smoothing of toric singularities, extending Lee-Park's complex case methods to positive characteristic.

Contribution

It generalizes Lee-Park's construction to positive characteristic and introduces a method for building simply connected surfaces of general type with specific invariants.

Findings

Constructed surfaces with p_g=q=0 and 1≤K^2≤4 in positive characteristic.

Extended complex case techniques to positive characteristic.

Demonstrated simply connectedness via Grothendieck's specialization theorem.

Abstract

Algebraically simply connected surfaces of general type with p_g=q=0 and 1\le K^2\le 4 in positive characteristic (with one exception in K^2=4) are presented by using a Q-Gorenstein smoothing of two-dimensional toric singularities, a generalization of Lee-Park's construction in the field of complex numbers to the positive characteristic case, and Grothendieck's specialization theorem for the fundamental group.