Hodge numbers of a Fano eightfold of K3 type

2025/12/16 by Vanja Zuliani, Zuliani, Vanja
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Geometry and complex manifolds #math.AG

paper · pdf · doi:10.48550/arxiv.2512.14249

openalex publication_date 2025/12/16 · openalex created_date 2025/12/18 · openalex updated_date 2026/07/28

Abstract

We construct an explicit semistable degeneration of a Fano eightfold of index three and deduce its Hodge numbers, in particular we show that it has Picard rank one. The Fano variety is of K3 type and it is defined as a connected component of the fixed locus of a suitable antisymplectic involution on a projective variety that is deformation equivalent to the Hilbert scheme of eight points on a K3 surface. We also obtain a description of a projective model of the Hilbert square of a K3 surface of genus eight in terms of secant lines to the surface.

Related

• Topics on Fano varieties of K3 type
• Hodge theory of cubic fourfolds, their Fano varieties, and associated K3 categories
• Derived categories of Fano varieties of lines
• Fano varieties of K3 type and IHS manifolds
• On K-moduli of Fano threefolds with degree 28 and Picard rank 4