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arXiv · 1801.02993

Construction of the Poincare sheaf for higher genus curves

Mao Li
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Abstract

Let $X$ be a smooth projective curve of genus $g$ and $L$ be a degree $l$ line bundle on $X$ with $l\geq 2g-1$. Denote the stack of rank two Higgs bundles on $X$ with value in $L$ by $\mathcal{H}iggs$ and the semistable part by $\mathcal{H}iggs_{ss}$. Let $H$ be the Hitchin base. In this paper we will construct the Poincare sheaf $\mathcal{P}$ on $\mathcal{H}iggs\times_{H}\mathcal{H}iggs_{ss}$ which is a maximal Cohen-Macaulay sheaf and flat over $\mathcal{H}iggs_{ss}$. In particular this includes the locus of nonreduced spectral curves.

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Mao Li. 2018-01-08. Construction of the Poincare sheaf for higher genus curves. https://arxiv.org/abs/1801.02993

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