Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Prof. Yunfeng Jiang，University of Kansas
Inviter:
Title:	The construction of virtual fundamental class on the moduli space of general type surfaces
Language:	Chinese
Time & Venue:	2023.06.20 10:40-11:40 MCM110 Zoom ID: 3329836068 Password: mcm1234
Abstract:	Professor Simon Donaldson conjectured that there should exist a virtual fundamental class on the moduli space of surfaces of general type inspired by the geometry of complex structures on the general type surfaces. In this talk I will present a method to construct the virtual fundamental class on the moduli stack of lci (locally complete intersection) covers over the moduli stack of general type surfaces with only semi-log-canonical singularities. A tautological invariant is defined by taking the integration of the power of the first Chern class of the CM line bundle over the virtual fundamental class. This can be taken as a generalization of the tautological invariants on the moduli space of stable curves to the moduli space of stable surfaces. If time permits, we also talk about the possible methods to construct a virtual fundamental class on the Alexeev moduli space of stable maps from semi-log-canonical surfaces to projective varieties.