Algebraic cycles and intersections of 2 quadrics

Abstract

A smooth intersection $Y$ of two quadrics in ${\mathbb{P}}^{2g+1}$ has Hodge level 1. We show that such varieties $Y$ have a multiplicative Chow-Künneth decomposition, in the sense of Shen-Vial. As a consequence, a certain tautological subring of the Chow ring of powers of $Y$ injects into cohomology.

arXiv comment21 pages, to appear in Mediterranean J. of Math., comments welcome. v2: minor changes to match published version. arXiv admin note: text overlap with arXiv:2009.11061

References in corpus (6)

• On the motive of some hyperKaehler varieties
• Projectors on the intermediate algebraic Jacobians
• On the Chow ring of Cynk-Hulek Calabi-Yau varieties and Schreieder varieties
• The generalized Franchetta conjecture for some hyper-Kähler varieties, II
• A remark on the Chow ring of Küchle fourfolds of type $d3$
• Algebraic cycles and Gushel-Mukai fivefolds

Cited by in corpus (2)

• Algebraic cycles and intersections of three quadrics
• On the tautological ring of Humbert curves