# Bloch's conjecture on certain surfaces of general type with $p_g=0$ and with an involution: the Enriques case

## TL;DR

This paper proves that involutions on certain surfaces of general type with geometric genus zero act trivially on zero cycles, confirming Bloch's conjecture for cases where the quotient surface is Enriques.

## Contribution

It demonstrates that involutions on specific surfaces with $p_g=0$ act as identity on zero cycles, supporting Bloch's conjecture in the Enriques case.

## Key findings

- Involutions act as identity on zero cycles for the studied surfaces.
- Bloch's conjecture holds for surfaces with Enriques quotient.
- The paper provides new evidence for Bloch's conjecture in the context of surfaces with involutions.

## Abstract

In this short note we prove that an involution on certain examples of surfaces of general type with $p_g=0$, acts as identity on the Chow group of zero cycles of the relevant surface. In particular we consider examples of such surfaces when the quotient is an Enriques surface and show that the Bloch's conjecture holds for such surfaces.