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

Let X be a smooth projective complex curve of genus g ≥ 2 and let MX(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 𝓦k ⊂ MX(2,Λ). We show that on one wobbly divisor the set of maximal subbundles is degenerate. We also compute the class of the divisors 𝓦k in the Picard group of MX(2, Λ). [ABSTRACT FROM AUTHOR]