A note on the Picard bundle over a moduli space of vector bundles

✍ Scribed by Indranil Biswas; L. Brambila–Paz

• Publisher: John Wiley and Sons
• Year: 2006
• Tongue: English
• Weight: 125 KB
• Volume: 279
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200310358

✦ Synopsis

Abstract

Let ℳ︁(n , d ) be a coprime moduli space of stable vector bundles of rank n ≥ 2 and degree d over a complex irreducible smooth projective curve X of genus g ≥ 2 and ℳ︁~ξ~ ⊂ ℳ︁(n , d ) a fixed determinant moduli space. Assuming that the degree d is sufficiently large, denote by 𝒦 the vector bundle over X ×ℳ︁(n , d ) defined by the kernel of the evaluation map H ^0^(X , E ) → E~x~ , where E ∈ℳ︁(n , d ) and x ∈ X . We prove that 𝒦 and its restriction 𝒦~ξ~ to X × ℳ︁__ξ__ are stable. The space of all infinitesimal deformations of 𝒦 over X ×ℳ︁(n , d ) is proved to be of dimension 3__g__ and that of 𝒦__ξ__ over X × ℳ︁__ξ__ of dimension 2__g__ , assuming that g ≥ 3 and if g = 3 then n ≥ 4 and if g = 4 then n ≥ 3. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)