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

2018/03/30 by Pal, Sarbeswar, Pauly, Christian
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1803.11315

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 \Ww_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 \Ww_k in the Picard group of \M_X(2,Λ).

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