2025/01/27 by Frédéric Han, Han, Frederic · 1 citation
Computer Science · Mathematics · #14J28 #14J32 #14J35 #14J70 #14M15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #Computational Geometry and Mesh Generation #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2501.16013
openalex publication_date 2025/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Polarized K3 surfaces of genus sixteen have a Mukai vector bundle of rank two. We study the geometry of the projectivization of this bundle. We prove that it has an embedding in ℙ9 with an ideal generated by quadrics. We give an effective method to compute these quadrics from a general choice in Mukai's unirationalization of the moduli space. This linear system gives a double cover of ℙ9 ramified on a degree 10 hypersurface. It gives relative Weddle/Kummer surfaces over a Peskine variety associated to an explicit trivector. This work is also motivated by hyperkähler geometry and Debarre-Voisin varieties. Oberdieck showed that the Hilbert square of a general K3-surface of genus 16 is a Debarre-Voisin variety for some trivector. We start to investigate the relationship between these two trivectors.