Construction of the Poincaré sheaf on the stack of rank two Higgs bundles of ${\mathbf{P}}^1$

Abstract

Let $\mathcal{H}igg{s}_{ss}$ be the stack of semistable rank two Higgs bundles on ${\mathbf{P}}^1$ with value in $O(n)$ where $n\ge 2$. In this paper we will construct the Poincaré sheaf $\mathcal{P}$ on $\mathcal{H}igg{s}_{ss}{\times }_H\mathcal{H}igg{s}_{ss}$ which is maximal Cohen-Macaulay and flat over $\mathcal{H}igg{s}_{ss}$.

36 pages

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