Restriction of the Poincaré bundle to a Calabi-Yau hypersurface

1999/02/25 by Indranil Biswas, Biswas, Indranil, L. Brambila‐Paz +2
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG

paper · pdf · doi:10.48550/arxiv.math/9902145

AMSLaTex file. To appear in Crelles J

arxiv created 1999/02/25 · openalex publication_date 1999/02/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \cMx be the moduli space of stable vector bundles of rank n≥ 3 and determinant ξ over a connected Riemann surface X, with n and d(ξ) coprime. Let D be a Calabi-Yau hypersurface of \cMx. Denote by U_D the restriction of the universal bundle to X× D. It is shown that the restriction (U_D)_x to x× D is stable, for any x∈ X. Furthermore, for a general curve the connected component of the moduli space of semistable sheaves over D, containing (U_D)_x, is isomorphic to X. It is also shown that U_D is stable for any polarisation, and the connected component of the moduli space of semistable sheaves over X× D, containing U_D, is isomorphic to the Jacobian. Moreover, this is an isomorphism of polarised varieties, and hence such a moduli spaces determine the Reimann surface.

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