The Picard group of a coarse moduli space of vector bundles in positive characteristic

• Autorzy: Norbert Hoffmann
• Języki publikacji: EN

Abstrakty

EN

Let C be a smooth projective curve over an algebraically closed field of arbitrary characteristic. Let M r,Lss denote the projective coarse moduli scheme of semistable rank r vector bundles over C with fixed determinant L. We prove Pic(M r,Lss) = ℤ, identify the ample generator, and deduce that M r,Lss is locally factorial. In characteristic zero, this has already been proved by Drézet and Narasimhan. The main point of the present note is to circumvent the usual problems with Geometric Invariant Theory in positive characteristic.

Słowa kluczowe

EN

Moduli space; Vector bundle; Picard group; Positive characteristic

Kategorie tematyczne

• 14H60: Vector bundles on curves and their moduli
• 14D20: Algebraic moduli problems, moduli of vector bundles

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 4
• Strony: 1306-1313

Daty

wydano

2012-08-01

online

2012-05-31

Twórcy

autor

Norbert Hoffmann

• Freie Universität Berlin

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-012-0064-0