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arXiv · 1803.11315

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

Sarbeswar Pal·Christian Pauly
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Abstract

Let $X$ be a smooth projective complex curve of genus $g \geq 2$ and let $\M_X(2,\Lambda)$ be the moduli space of semi-stable rank-$2$ vector bundles over $X$ with fixed determinant $\Lambda$. 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 $\Ww_k \subset \M_X(2,\Lambda)$. 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 $\M_X(2,\Lambda)$.

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Sarbeswar Pal, Christian Pauly. 2018-03-30. The wobbly divisors of the moduli space of rank-$2$ vector bundles. https://arxiv.org/abs/1803.11315

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