Some Motivic Properties of Gushel-Mukai Sixfolds
Michele Bolognesi, Robert Laterveer
TL;DR
This paper proves that Gushel-Mukai sixfolds, a class of Fano-K3 varieties, have a multiplicative Chow-K"unneth decomposition and the Franchetta property, with additional results on related varieties and Chow ring vanishing.
Contribution
It establishes the multiplicative Chow-K"unneth decomposition and Franchetta property for Gushel-Mukai sixfolds, advancing understanding of their algebraic cycles.
Findings
Gushel-Mukai sixfolds admit a multiplicative Chow-K"unneth decomposition
They possess the Franchetta property modulo algebraic equivalence
Double EPW sextics and cubes also have the Franchetta property
Abstract
Gushel-Mukai sixfolds are an important class of so-called Fano-K3 varieties. In this paper we show that they admit a multiplicative Chow-K\"unneth decomposition modulo algebraic equivalence and that they have the Franchetta property. As side results, we show that double EPW sextics and cubes have the Franchetta property, modulo algebraic equivalence, and some vanishing results for the Chow ring of Gushel-Mukai sixfolds.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Combinatorial Mathematics · Advanced Algebra and Geometry