no. 3
Algebraic geometry/Topology
An integrable connection on the configuration space of a Riemann surface of positive genus
[Une connexion intégrable sur l'espace de configuration d'une surface de Riemann de genre positif]

Présenté par : Claire Voisin

Eskandari, Payman1
1 Department of Mathematics, University of Toronto, 40 St. George St., Room 6290, Toronto, Ontario, M5S 2E4, Canada
Comptes Rendus. Mathématique, Tome 356 (2018) no. 3, pp. 312-315.

Soit X une surface de Riemann de genre positif. Nous notons X(n) l'espace des configurations de n points distincts sur X. Nous utilisons l'isomorphisme de comparaison de Betti–de Rham sur H1(X(n)) pour définir une connexion intégrable sur le fibré vectoriel trivial sur X(n), dont la fibre est l'algèbre universelle de l'algèbre de Lie associée à la série centrale descendante du π1 de X(n). La construction s'inspire du système de Knizhnik–Zamolodchikov en genre zéro ; l'intégrabilité résulte des relations de périodes de Riemann.

Let X be a Riemann surface of positive genus. Denote by X(n) the configuration space of n distinct points on X. We use the Betti–de Rham comparison isomorphism on H1(X(n)) to define an integrable connection on the trivial vector bundle on X(n) with fiber the universal algebra of the Lie algebra associated with the descending central series of π1 of X(n). The construction is inspired by the Knizhnik–Zamolodchikov system in genus zero and its integrability follows from Riemann period relations.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2018.02.003
Eskandari, Payman 1

1 Department of Mathematics, University of Toronto, 40 St. George St., Room 6290, Toronto, Ontario, M5S 2E4, Canada 
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Eskandari, Payman. An integrable connection on the configuration space of a Riemann surface of positive genus. Comptes Rendus. Mathématique, Tome 356 (2018) no. 3, pp. 312-315. doi : 10.1016/j.crma.2018.02.003. http://archive.numdam.org/articles/10.1016/j.crma.2018.02.003/

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