Hyperkähler varieties as Brill-Noether loci on curves

2022/05/02 by Soheyla Feyzbakhsh, Feyzbakhsh, Soheyla
Mathematics · Social Sciences · #14H60 #14J28 #18E30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Vietnamese History and Culture Studies

paper · pdf · doi:10.48550/arxiv.2205.00681

openalex publication_date 2022/05/02 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

Consider the moduli space M_C(r; K_C) of stable rank r vector bundles on a curve C with canonical determinant, and let h be the maximum number of linearly independent global sections of these bundles. If C embeds in a K3 surface X as a generator of Pic(X) and the genus g of C is sufficiently high, we show the Brill-Noether locus BN_C ⊂ M_C(r; K_C) of bundles with h global sections is a smooth projective Hyperkähler manifold of dimension 2g -2r \lfloor (g)/(r)\rfloor, isomorphic to a moduli space of stable vector bundles on X.

Related

• Maximal Brill-Noether loci via K3 surfaces
• Brill--Noether loci on moduli spaces of symplectic bundles over curves
• Mukai's program for non-primitive curves on K3 surfaces
• Brill--Noether loci of stable rank--two vector bundles on a general curve
• Brill-Noether Theory of stable vector bundles on ruled surfaces