Bloch's conjecture on surfaces of general type with an involution

TL;DR

This paper proves Bloch's conjecture for certain complex surfaces of general type with involution, specifically when the quotient surface is rational, extending the class of surfaces where the conjecture holds.

Contribution

It establishes Bloch's conjecture for surfaces of general type with involution and rational quotient surfaces, covering numerical Godeaux and Campedelli types.

Findings

Bloch's conjecture holds for these surfaces with involution.

The quotient surface being rational is key to the proof.

Extends known cases where the conjecture is verified.

Abstract

In this short note we prove that the Bloch's conjecture holds for a surface of general type of numerical Godeaux type or some class of numerical Campedelli type, with geometric genus zero equipped with an involution, when the quotient of the surface by the involution is a rational surface.