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Fundamental group schemes of some Quot schemes on a smooth projective curve. (English) Zbl 1441.14151

Summary: Let \(k\) be an algebraically closed field. Let \(C\) be an irreducible smooth projective curve over \(k\). Let \(E\) be a locally free sheaf on \(C\) of rank \(\geq 2\). Fix an integer \(d \geq 2\). Let \(\mathcal{Q}\) denote the Quot scheme parameterizing torsion quotients of \(E\) of degree \(d\). In this article we compute the \(S\)-fundamental group scheme of \(\mathcal{Q} \).

MSC:

14L15 Group schemes
14C05 Parametrization (Chow and Hilbert schemes)
14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
14F35 Homotopy theory and fundamental groups in algebraic geometry
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References:

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