The wobbly divisors of the moduli space of rank-2 vector bundles

Author:

Pal Sarbeswar1,Pauly Christian2

Affiliation:

1. Indian Institute of Science Education and Research , Thiruvananthapuram, Maruthamala PO, Vithura, Thiruvananthapuram - 695551 , Kerala , India

2. Laboratoire de Mathématiques J.A. Dieudonné, UMR 7351 CNRS , Université de Nice Sophia-Antipolis , 06108 Nice Cedex 02 , Nice , France

Abstract

Abstract Let X be a smooth projective complex curve of genus g ≥ 2 and let M X (2,Λ) be the moduli space of semi-stable rank-2 vector bundles over X with fixed determinant Λ. We show that the wobbly locus, i.e. the locus of semi-stable vector bundles admitting a non-zero nilpotent Higgs field, is a union of divisors 𝓦 k ⊂ M X (2,Λ). We show that on one wobbly divisor the set of maximal subbundles is degenerate. We also compute the class of the divisors 𝓦 k in the Picard group of M X (2, Λ).

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

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