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The NY Gravity operad and the Deligne—Mumford stack with hidden symmetry

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Noémie Combe
MPI MiS, Leipzig
Die, 06/10/2020 - 14:00 - 15:00
A paracomplex Deligne—Mumford stack is considered. This structure introduces additional conical singularities, in the neighbourhood of which the curvature is negative. In particular, properties are investigated and we establish a relationship between the paracomplex Deligne—Mumford stack and classical Deligne—Mumford stack. Moreover, we show that the  NY Gravity operad  associated to this space (introduced by Manin and Combe) has a mixed Hodge structure. In this framework, the strong Hodge theorem extends and the pure Hodge structure (Kähler package) holds. Since we use tools from L^2 cohomology, a parallel with the model of Atiyah—Hitchin and  Donaldson is established.
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