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Seshadri constants on some Quot schemes

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Abstract Let E be a vector bundle of rank n on ℙ1{\mathbb{P}^{1}}. Fix a positive integer d. Let ????⁢(E,d){\mathcal{Q}(E,d)} denote the Quot scheme of torsion quotients of E of degree… Click to show full abstract

Abstract Let E be a vector bundle of rank n on ℙ1{\mathbb{P}^{1}}. Fix a positive integer d. Let ????⁢(E,d){\mathcal{Q}(E,d)} denote the Quot scheme of torsion quotients of E of degree d and let Gr⁢(E,d){\mathrm{Gr}(E,d)} denote the Grassmann bundle that parametrizes the d-dimensional quotients of the fibers of E. We compute Seshadri constants of ample line bundles on ????⁢(E,d){\mathcal{Q}(E,d)} and Gr⁢(E,d){\mathrm{Gr}(E,d)}.

Keywords: quot schemes; constants quot; seshadri constants

Journal Title: Forum Mathematicum
Year Published: 2021

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