On the geometry of moduli of curves and line bundles

Claudio Fontanari

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2005)

  • Volume: 16, Issue: 1, page 45-59
  • ISSN: 1120-6330

Abstract

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Here we focus on the geometry of P ¯ d , g , the compactification of the universal Picard variety constructed by L. Caporaso. In particular, we show that the moduli space of spin curves constructed by M. Cornalba naturally injects into P ¯ d , g and we give generators and relations of the rational Picard group of P ¯ d , g , extending previous work by A. Kouvidakis.

How to cite

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Fontanari, Claudio. "On the geometry of moduli of curves and line bundles." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 16.1 (2005): 45-59. <http://eudml.org/doc/252379>.

@article{Fontanari2005,
abstract = {Here we focus on the geometry of $\overline\{P\}_\{d,g\}$, the compactification of the universal Picard variety constructed by L. Caporaso. In particular, we show that the moduli space of spin curves constructed by M. Cornalba naturally injects into $\overline\{P\}_\{d,g\}$ and we give generators and relations of the rational Picard group of $\overline\{P\}_\{d,g\}$, extending previous work by A. Kouvidakis.},
author = {Fontanari, Claudio},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Universal Picard variety; Geometric invariant theory; Spin curve; Stable curve; universal Picard variety; geometric invariant theory; spin curve; stable curve},
language = {eng},
month = {3},
number = {1},
pages = {45-59},
publisher = {Accademia Nazionale dei Lincei},
title = {On the geometry of moduli of curves and line bundles},
url = {http://eudml.org/doc/252379},
volume = {16},
year = {2005},
}

TY - JOUR
AU - Fontanari, Claudio
TI - On the geometry of moduli of curves and line bundles
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2005/3//
PB - Accademia Nazionale dei Lincei
VL - 16
IS - 1
SP - 45
EP - 59
AB - Here we focus on the geometry of $\overline{P}_{d,g}$, the compactification of the universal Picard variety constructed by L. Caporaso. In particular, we show that the moduli space of spin curves constructed by M. Cornalba naturally injects into $\overline{P}_{d,g}$ and we give generators and relations of the rational Picard group of $\overline{P}_{d,g}$, extending previous work by A. Kouvidakis.
LA - eng
KW - Universal Picard variety; Geometric invariant theory; Spin curve; Stable curve; universal Picard variety; geometric invariant theory; spin curve; stable curve
UR - http://eudml.org/doc/252379
ER -

References

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  6. CAPORASO, L. - CASAGRANDE, C. - CORNALBA, M., Moduli of roots of line bundles on curves. Preprint math.AG/0404078, 2004. Zbl1140.14022MR2302513DOI10.1090/S0002-9947-07-04087-1
  7. CAPORASO, L. - SERNESI, E., Recovering plane curves from their bitangents. J. Algebraic Geom., 12, 2003, 225-244. Zbl1080.14523MR1949642DOI10.1090/S1056-3911-02-00307-7
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  9. CORNALBA, M., Moduli of curves and theta-characteristics. In: M. CORNALBA - X. GOMEZ-MONT - A. VERJOVSKY (eds.), Lectures on Riemann surfaces (Trieste 1987). World Sci. Publishing, Singapore1989, 560-589. Zbl0800.14011MR1082361
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