Rigid surfaces arbitrarily close to the Bogomolov--Miyaoka--Yau line

TL;DR

This paper constructs new examples of rigid compact complex surfaces of general type with Chern slopes approaching the theoretical maximum of 3, all having first Betti number 4, advancing understanding of surface geometry near the Bogomolov--Miyaoka--Yau line.

Contribution

It demonstrates the existence of rigid surfaces with Chern slopes arbitrarily close to 3, each with first Betti number 4, near the Bogomolov--Miyaoka--Yau bound.

Findings

Existence of rigid surfaces with Chern slopes approaching 3

Surfaces have first Betti number equal to 4

Advances understanding of surfaces near the Bogomolov--Miyaoka--Yau line

Abstract

We prove the existence of rigid compact complex surfaces of general type whose Chern slopes are arbitrarily close to the Bogomolov--Miyaoka--Yau bound of $3$. In addition, each of these surfaces has first Betti number equal to $4$.