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.

Reçu le : 2011-04-01
Révisé le : 2012-06-10
Accepté le : 2012-08-30
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
@article{AIF_2013__63_4_1469_0,
     author = {Pagani, Nicola},
     title = {Chen--Ruan Cohomology of $\mathcal{M}\_{1,n}$ and $\overline{\mathcal{M}}\_{1,n}$},
     journal = {Annales de l'Institut Fourier},
     pages = {1469--1509},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {63},
     number = {4},
     year = {2013},
     doi = {10.5802/aif.2808},
     zbl = {06359594},
     mrnumber = {3137360},
     language = {en},
     url = {aif.centre-mersenne.org/item/AIF_2013__63_4_1469_0/}
}
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/item/AIF_2013__63_4_1469_0/

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