Smoothness of Moduli Space of Stable Torsion-free Sheaves with Fixed Determinant in Mixed Characteristic

Inder Kaur ()
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Inder Kaur: Freie Universitaet Berlin, FB Mathematik und Informatik

A chapter in Analytic and Algebraic Geometry, 2017, pp 173-186 from Springer

Abstract: Abstract Let $$ R $$ be a complete discrete valuation ring with fraction field of characteristic 0 and algebraically closed residue field of characteristic $$ p > 0 $$ . Let $$ X_{R} \to {\text{Spec}}(R) $$ be a smooth projective morphism of relative dimension 1. We prove that, given a line bundle $$ {\mathcal{L}}_{{\mathcal{R}}} $$ the moduli space of Gieseker stable torsion-free sheaves of rank $$ r \ge 2 $$ over $$ X_{R} $$ , with determinant $$ {\mathcal{L}}_{{\mathcal{R}}} $$ , is smooth over $$ R $$ .

Date: 2017
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DOI: 10.1007/978-981-10-5648-2_11

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