18:10 Семинар Международной лаборатории кластерной геометрии: Денис Лысков

Moduli spaces of stable curves associated with graphs

The Deligne-Mumford moduli spaces of stable curves with marked points are central objects in mathematical physics, specifically in Gromov-Witten theory. In the genus zero case, these moduli spaces are indeed the complex smooth projective varieties.
In addition to the Deligne-Mumford compactification, there are alternative compactifications, for example, the Hasset and Losev-Manin compactifications in which some marked points may "stick together". In this report, we discuss a new class of alternative compactifications ( in the genus zero case) associated with graphs that are specific blow-downs of the classical compactifications.
We explain the construction of these moduli spaces and their internal geometry, including the description of cohomology rings. Mimicking Getzler’s strategy based on operadic methods, we deduce the functional equations for the generating series of Hilbert series of graphic compactifications.
At the end of the report, we discuss some properties of psi-classes for graphic compactifications and consider partial results concerning their intersection numbers.
This talk is based on the joint work with A. Khoroshkin https://arxiv.org/abs/2406.05909