A remark on the Picard group of spin moduli space

Maurizio Cornalba

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On the geometry of moduli of curves and line bundles

Claudio Fontanari (2005)

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

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Here we focus on the geometry of ${\bar{P}}_{d, g}$ , 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 ${\bar{P}}_{d, g}$ and we give generators and relations of the rational Picard group of ${\bar{P}}_{d, g}$ , extending previous work by A. Kouvidakis.