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

Norbert Hoffmann

Open Mathematics (2012)

  • Volume: 10, Issue: 4, page 1306-1313
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Norbert Hoffmann. "The Picard group of a coarse moduli space of vector bundles in positive characteristic." Open Mathematics 10.4 (2012): 1306-1313. <http://eudml.org/doc/269083>.

@article{NorbertHoffmann2012,
abstract = {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.},
author = {Norbert Hoffmann},
journal = {Open Mathematics},
keywords = {Moduli space; Vector bundle; Picard group; Positive characteristic; moduli space; vector bundle; positive characteristic},
language = {eng},
number = {4},
pages = {1306-1313},
title = {The Picard group of a coarse moduli space of vector bundles in positive characteristic},
url = {http://eudml.org/doc/269083},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Norbert Hoffmann
TI - The Picard group of a coarse moduli space of vector bundles in positive characteristic
JO - Open Mathematics
PY - 2012
VL - 10
IS - 4
SP - 1306
EP - 1313
AB - 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.
LA - eng
KW - Moduli space; Vector bundle; Picard group; Positive characteristic; moduli space; vector bundle; positive characteristic
UR - http://eudml.org/doc/269083
ER -

References

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