Vector bundles on Fano varieties of genus ten

2010/05/30 by Grzegorz Kapustka, Kristian Ranestad, Kapustka, Michal +1
Mathematics · #14J28 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Primary: 14D20 #Secondary: 14J45

paper · pdf · doi:10.48550/arxiv.1005.5528

openalex publication_date 2010/05/30 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

In this note we describe a unique linear embedding of a prime Fano 4-fold F of genus 10 into the Grassmannian G(3,6). We use this to construct some moduli spaces of bundles on linear sections of F. In particular the moduli space of bundles with Mukai vector (3,L,3) on a generic polarized K3 surface (S,L) of genus 10 is constructed as a double cover of the projective plane branched over a smooth sextic.

Related

• Elliptic curves and rank-2 vector bundles on the prime Fano threefold of genus 7
• Mukai bundles on Fano threefolds
• Geometry of genus 9 Fano 4-fold
• K-moduli of Fano threefolds and genus four curves
• Vector bundles on a K3 surface