Algebraic Cycles and Intersections of 2 Quadrics

2021/05/31 by Robert Laterveer · 4 citations
Computer Science · Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic number #Closure (psychology) #Commutative Algebra and Its Applications #Complete intersection #Intersection (aeronautics) #Multiplicative function #Polynomial and algebraic computation #Ring (chemistry) #Subring #math.AG #msc:14C15 #msc:14C25 #msc:14C30

paper · pdf · doi:10.1007/s00009-021-01787-5

published in Mediterranean Journal of Mathematics 18(4) (Birkhäuser) · 21 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

openalex created_date 2021/05/10 · openalex publication_date 2021/06/05 · arxiv created 2021/06/10 · arxiv updated 2021/06/11 · openalex updated_date 2026/08/05

Abstract

A smooth intersection Y of two quadrics in 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.

Citations

• Algebraic cycles and Gushel-Mukai fivefolds
• On a conjectural filtration on the Chow groups of an algebraic variety
• The generalized Franchetta conjecture for some hyper-Kähler varieties, II

Cited by

• Some new Fano varieties with a multiplicative Chow-Künneth decomposition
• Algebraic cycles and Fano threefolds of genus 8