Bloch's conjecture on surfaces with $p_g=q=0, K^2=9$

TL;DR

This paper proves Bloch's conjecture for a specific class of complex surfaces characterized by geometric genus and irregularity zero and a particular self-intersection number of the canonical divisor.

Contribution

It establishes the validity of Bloch's conjecture for surfaces with $p_g=q=0$ and $K^2=9$, expanding the class of surfaces where the conjecture is confirmed.

Findings

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

The proof confirms conjecture for a new class of surfaces

Advances understanding of algebraic cycles on complex surfaces

Abstract

In this paper, we prove that Bloch's conjecture holds for all smooth, complex, projective surfaces with $p_g=q=0$ and $K^2=9$.