Some surfaces of general type for which Bloch's conjecture holds

TL;DR

This paper provides numerous examples of surfaces of general type with geometric genus zero where Bloch's conjecture is verified, except for the case when the self-intersection number of the canonical divisor is 9.

Contribution

It constructs and verifies Bloch's conjecture for a wide class of surfaces with involutions, expanding known cases where the conjecture holds.

Findings

Bloch's conjecture verified for surfaces with $p_g=0$ and $K^2 eq 9$

Constructs explicit examples of such surfaces with involutions

Extends the class of surfaces where Bloch's conjecture is confirmed

Abstract

We give many examples of surfaces of general type with $p_g=0$ for which Bloch's conjecture holds, for all values of $K^2$ except 9. Our surfaces are equipped with an involution.