Bloch's conjecture for some numerical Campedelli surfaces

TL;DR

This paper proves Bloch's conjecture for a specific class of algebraic surfaces known as numerical Campedelli surfaces with a fundamental group of order 9, advancing understanding in algebraic geometry.

Contribution

It establishes Bloch's conjecture for numerical Campedelli surfaces with fundamental group of order 9, a case previously unresolved.

Findings

Bloch's conjecture holds for these surfaces

Provides new insights into the structure of numerical Campedelli surfaces

Enhances understanding of algebraic cycles on complex surfaces

Abstract

We prove Bloch's conjecture for numerical Campedelli surfaces with fundamental group of order $9$.