Displaying similar documents to “Calculating cohomology groups of moduli spaces of curves via algebraic geometry”

The fourth tautological group of M ¯ g , n and relations with the cohomology

Marzia Polito (2003)

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

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We give a complete description of the fourth tautological group of the moduli space of pointed stable curves, M ¯ g , n , and prove that for g ≥ 8 it coincides with the cohomology group with rational coefficients. We further give a conjectural upper bound depending on the genus for the degree of new tautological relations.

A remark on the Picard group of spin moduli space

Maurizio Cornalba (1991)

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

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We describe a number of classes in the Picard group of spin moduli space and determine the relations they satisfy; as an application we show that the Picard group in question contains 4-torsion elements.