Infinitesimal deformations of a Calabi-Yau hypersurface of the moduli space of stable vector bundles over a curve

1999/04/08 by Indranil Biswas, Biswas, Indranil, Leticia Brambila-Paz +1
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/9904033

AMS-LaTex file

arxiv created 1999/04/08 · arxiv updated 2009/11/30

Abstract

Let X be a compact connected Riemann surface of genus g, with g≥ 2, and \cal M_ξ a smooth moduli space of fixed determinant semistable vector bundles of rank n, with n≥ 2, over X. Take a smooth anticanonical divisor D on \cal M_ξ. So D is a Calabi-Yau variety. We compute the number of moduli of D, namely dim H¹(D, T_D), to be 3g-4 + dim H⁰(\cal M_ξ, K^-1_\cal M_ξ). Denote by \cal N the moduli space of all such pairs (X',D'), namely D' is a smooth anticanonical divisor on a smooth moduli space of semistable vector bundles over the Riemann surface X'. It turns out that the Kodaira-Spencer map from the tangent space to \cal N, at the point represented by the pair (X,D), to H¹(D, T_D) is an isomorphism. This is proved under the assumption that if g =2, then n≠ 2,3, and if g=3, then n≠ 2.

Related

• Restriction of the Poincaré bundle to a Calabi-Yau hypersurface
• Hodge structures of the moduli spaces of pairs
• A Compactification Over M_g Of The Universal Moduli Space of Slope-Semistable Vector Bundles
• The automorphism group of the moduli space of semi stable vector bundles
• Moduli of high rank Vector bundles over Surface