Savage Surfaces

TL;DR

This paper proves that for any given fundamental group of a complex projective surface, the Chern slopes of minimal surfaces with that group are densely distributed between 1 and 3.

Contribution

It establishes the density of Chern slopes in [1,3] for minimal surfaces of general type with a fixed fundamental group.

Findings

Chern slopes are dense in [1,3] for given fundamental groups.

The result applies to minimal nonsingular projective surfaces of general type.

Provides new insights into the geography of complex surfaces.

Abstract

Let $G$ be the topological fundamental group of a given nonsingular complex projective surface. We prove that the Chern slopes $c_1^2(S)/c_2(S)$ of minimal nonsingular projective surfaces of general type $S$ with $\pi_1(S) \simeq G$ are dense in the interval $[1,3]$.