Motivic cycles on K3 double covers of del Pezzo surfaces

2024/11/06 by Ramesh Sreekantan, Sreekantan, Ramesh
Mathematics · #14C25 #14G35 14J28 #19E15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2411.03704

openalex publication_date 2024/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct motivic cohomology cycles in the group H³_{\mathcal M}(Z,\mathbb Q(2)) where Z is a K3 surface obtained as a double cover of a del Pezzo surface X branched at a curve in |-2K_X|. The construction uses (-1) curves on the del Pezzo and is a generalization of a recent pre-print of Ken Sato arXiv: 2408.09102 where he considers the case of fourfold covers of \mathbb P² branched at a quartic curve.

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