SIMIS Seminar on Algebraic Geometry: COHOMOLOGICAL ASPECT OF MODULI OF 1D SHEAVES ON SURFACES

Speaker: Fei Si (Xi’an Jiaotong University)

Abstract: Cohomology of moduli spaces of 1 dimensional sheaves on del Pezzo surfaces X is expected to refine enumerative geometry of the local Calabi-Yau 3-folds Tot(ω_X). On the one hand, the normalized generators of the cohomology of moduli space will induce Chern filtration on the cohomology. On the other hand, Hilbert-Chow morphism on moduli space will produce perverse filtration, whose graded dimension is called refined BPS number of the local del Pezzo surface. As an analogue of famous ”P=W” conjecture, it is conjectured by Kononov-Pi-Shen and Kononov-Lim-Moreira-Pi that Chern filtration and perverse filtration coincide, i.e., ”P=C”.

In this talk I will report the recent progress on the ”P=C” conjecture. Based on joint work with Weite Pi, Junliang Shen and Feinuo Zhang.

Time: 11:00-12:00, Tuesday, Oct. 15, 2024

Location: Room 1610, Block A, No. 657 Songhu Road, Yangpu District, Shanghai