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

Pagani, Nicola

doi:10.5802/aif.2808

Chen–Ruan Cohomology of

ℳ_{1, n}

and

{\bar{ℳ}}_{1, n}

[Cohomologie de Chen–Ruan de

ℳ_{1, n}

{\bar{ℳ}}_{1, n}

]

Pagani, Nicola ¹

¹ Institut fur Algebraische Geometrie, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany

Annales de l'Institut Fourier, Tome 63 (2013) no. 4, pp. 1469-1509.

Résumé
Abstract

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 $ℳ_{1, n}$ et ${\bar{ℳ}}_{1, n}$ , en tant que champs.

Dans la deuxième partie, on étudie la théorie d’intersection orbifold de ${\bar{ℳ}}_{1, n}$ . 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.

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 $ℳ_{1, n}$ and ${\bar{ℳ}}_{1, n}$ . In the second part, we study the orbifold intersection theory of ${\bar{ℳ}}_{1, n}$ . 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.

MR Zbl

DOI : 10.5802/aif.2808

Classification : 14H10, 14N35, 55N32, 14D23, 14H37, 55P50
Keywords: moduli spaces, Gromov-Witten, orbifold, cohomology, tautological ring
Mot clés : espaces de modules, Gromov-Witten, orbifold, cohomologie, anneau tautologique

Affiliations des auteurs :

Pagani, Nicola ¹

¹ Institut fur Algebraische Geometrie, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany

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Pagani, Nicola. Chen–Ruan Cohomology of $\mathcal{M}_{1,n}$ and $\overline{\mathcal{M}}_{1,n}$. Annales de l'Institut Fourier, Tome 63 (2013) no. 4, pp. 1469-1509. doi : 10.5802/aif.2808. https://aif.centre-mersenne.org/articles/10.5802/aif.2808/

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