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Tautological relations and the r -spin Witten conjecture

Carel Faber, Sergey Shadrin, Dimitri Zvonkine (2010)

Annales scientifiques de l'École Normale Supérieure

In [11], A. Givental introduced a group action on the space of Gromov–Witten potentials and proved its transitivity on the semi-simple potentials. In [24, 25], Y.-P. Lee showed, modulo certain results announced by C. Teleman, that this action respects the tautological relations in the cohomology ring of the moduli space ℳ ¯ g , n of stable pointed curves. Here we give a simpler proof of this result. In particular, it implies that in any semi-simple Gromov–Witten theory where arbitrary correlators can be...

The automorphism group of M ¯ 0 , n

Andrea Bruno, Massimiliano Mella (2013)

Journal of the European Mathematical Society

The paper studies fiber type morphisms between moduli spaces of pointed rational curves. Via Kapranov’s description we are able to prove that the only such morphisms are forgetful maps. This allows us to show that the automorphism group of M ¯ 0 , n is the permutation group on n elements as soon as n ≥ 5 .

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

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.

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