Chen–Ruan Cohomology of 1,n and ¯ 1,n
[Cohomologie de Chen–Ruan de 1,n et ¯ 1,n ]
Annales de l'Institut Fourier, Tome 63 (2013) no. 4, pp. 1469-1509.

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 1,n et ¯ 1,n , en tant que champs.

Dans la deuxième partie, on étudie la théorie d’intersection orbifold de ¯ 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 1,n and ¯ 1,n . In the second part, we study the orbifold intersection theory of ¯ 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.

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
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. http://www.numdam.org/articles/10.5802/aif.2808/

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