2025/04/29 by Yingqi Liu, Liu, Yingqi, Laurent Manivel +1 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebraic Geometry (math.AG) #Algebraic and Geometric Analysis #FOS: Mathematics #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2504.21056
openalex publication_date 2025/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Following previous work by A. Kuznetsov, we study the Fano manifolds obtained as linear sections of the spinor tenfold in ℙ15. Up to codimension three there are finitely many such sections, up to projective equivalence. In codimension four there are three moduli, and this family is particularly interesting because of its relationship with Kummer surfaces on the one hand, and a grading of the exceptional Lie algebra \mathfrake8 on the other hand. We show how the two approaches are intertwined, and we prove that codimension four sections of the spinor tenfolds and Kummer surfaces have the very same GIT moduli space. The Lie theoretic viewpoint provides a wealth of additional information. In particular we locate and study the unique section admitting an action of SL2× SL2; similarly to the Mukai-Umemura variety in the family of prime Fano threefold of genus 12, it is a compactification of a quotient by a finite group.