On the Chow ring of birational irreducible symplectic varieties

By Ulrike Riess. 2013

55 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/598e4903036672ced4aa6b6bc3c6f9ba98d538eb

How researchers see this paper

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In Geometry and Topology

1. M. Shen
2. L. Fu
3. Charles Vial
4. Robert Laterveer

In Mathematical Physics

1. M. Shen
2. L. Fu
3. Charles Vial
4. Robert Laterveer

Citations in the corpus

• THE MOTIVE OF THE HILBERT CUBE $X^{[3]}$ (2015, background): “When the ground field k has characteristic zero, Riess [11] showed that birational hyperKähler varieties have isomorphic Chow rings and isomorphic Chow motives as algebras in the category of Chow motives.”
• The generalized Franchetta conjecture for some hyper-Kähler varieties, II (2020, background): “First, as two bi-rationally isomorphic hyper-Kähler varieties have isomorphic Chow motives [Rie14], it is enough to consider the crepant resolution constructed by O’Grady and Lehn– Sorger.”