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

Pagani, Nicola

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

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

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 ${\overline{ℳ}}_{1,n}$, en tant que champs.

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

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

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