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Brauer groups of Quot schemes. (English) Zbl 1327.14097

Summary: Let \(X\) be an irreducible smooth complex projective curve. Let \(\mathcal{Q}(r,d)\) be the Quot scheme parameterizing all coherent subsheaves of \(\mathcal{O}_X^{\oplus r}\) of rank \(r\) and degree \(-d\). There are natural morphisms \(\mathcal{Q}(r,d) \longrightarrow \mathrm{Sym}^d (X)\) and \(\mathrm{Sym}^d(X)\longrightarrow \mathrm{Pic}^d(X)\). We prove that both these morphisms induce isomorphism of Brauer groups if \(d\geq 2\). Consequently, the Brauer group of \(\mathcal{Q}(r,d)\) is identified with the Brauer group of \(\mathrm{Pic}^d(X)\) if \(d\geq 2\).

MSC:

14F22 Brauer groups of schemes
14C05 Parametrization (Chow and Hilbert schemes)
14D23 Stacks and moduli problems
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References:

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