Curve classes on irreducible holomorphic symplectic varieties

TL;DR

This paper proves the integral Hodge conjecture for 1-cycles on specific types of irreducible holomorphic symplectic varieties, providing new insights and applications to cubic fourfolds.

Contribution

It establishes the integral Hodge conjecture for 1-cycles on K3 type and Generalized Kummer type varieties, and offers a new proof for cubic fourfolds.

Findings

Proves the integral Hodge conjecture for 1-cycles on K3 and Generalized Kummer types.

Provides a new proof of the conjecture for cubic fourfolds.

Advances understanding of algebraic cycles on holomorphic symplectic varieties.

Abstract

We prove that the integral Hodge conjecture holds for 1-cycles on irreducible holomorphic symplectic varieties of K3 type and of Generalized Kummer type. As an application, we give a new proof of the integral Hodge conjecture for cubic fourfolds.