Chen–Ruan Cohomology of $\mathcal{M}_{1,n}$ and $\overline{\mathcal{M}}_{1,n}$

[Cohomologie de Chen–Ruan de $\mathcal{M}_{1,n}$ et $\overline{\mathcal{M}}_{1,n}$]

Pagani, Nicola

Annales de l'Institut Fourier, Tome 63 (2013), p. 1469-1509 / Harvested from Numdam

Résumé

Dans ce travail on calcule la cohomologie de Chen–Ruan de l’espace de modules des courbes lisses et stables de genre $1$ avec $n$ points marqués. Dans la première partie on étudie et on décrit les secteurs tordus de $\mathcal{M}_{1,n}$ et $\overline{\mathcal{M}}_{1,n}$, en tant que champs.

Dans la deuxième partie, on étudie la théorie d’intersection orbifold de $\overline{\mathcal{M}}_{1,n}$. On donne une définition possible de l’anneau tautologique orbifold en genre $1$, comme sous-anneau simultanément de la cohomologie de Chen–Ruan et de l’anneau de Chow orbifold.

Abstract

In this work we compute the Chen–Ruan cohomology of the moduli spaces of smooth and stable $n$-pointed curves of genus $1$. In the first part of the paper we study and describe stack theoretically the twisted sectors of $\mathcal{M}_{1,n}$ and $\overline{\mathcal{M}}_{1,n}$. In the second part, we study the orbifold intersection theory of $\overline{\mathcal{M}}_{1,n}$. We suggest a definition for an orbifold tautological ring in genus $1$, which is a subring of both the Chen–Ruan cohomology and of the stringy Chow ring.

Détail

Publié le : 2013-01-01

MR 3137360 | Zbl 06359594

DOI : https://doi.org/10.5802/aif.2808
Classification:  14H10,  14N35,  55N32,  14D23,  14H37,  55P50
Mots clés: espaces de modules, Gromov-Witten, orbifold, cohomologie, anneau tautologique

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