Rational homotopy type of the moduli space of stable rational curves

Vladimir Dotsenko
Université de Strasbourg

Date(s) : 14/09/2023   iCal
11 h 00 min - 12 h 00 min

In 2004, Manin asked whether the cohomology of the moduli space of stable rational curves with n marked points (= the Deligne-Mumford compactification of the moduli space of smooth genus zero curves with n marked points) is a Koszul algebra. I shall present a complete solution to this problem, proving that the answer is positive for all n. An immediate consequence of my result is an explicit description of the rational homotopy Lie algebras of these spaces by generators and relations. Time permitting, I shall discuss some generalizations and modifications of this result obtained by Basile Coron in his PhD thesis defended this year.


Salle de séminaire de l'I2M à St Charles


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