On the Chow ring of birational irreducible symplectic varieties

TL;DR

This paper proves that birational irreducible symplectic varieties have isomorphic graded Chow rings, extending known cohomology results to Chow rings, with explicit calculations for Mukai flops.

Contribution

It establishes the isomorphism of Chow rings for birational irreducible symplectic varieties, advancing understanding beyond cohomology to Chow rings.

Findings

Chow rings of birational irreducible symplectic varieties are isomorphic.

Extension of cohomology results to Chow rings.

Explicit calculations for Mukai flops.

Abstract

We show that the graded Chow rings of two birational irreducible symplectic varieties are isomorphic. This lifts a result known for the cohomology algebras to the level of Chow rings, despite the non-injectivity the cycle class map. In the special case of general Mukai flops, we present an alternative approach based on explicit calculations.