Title: Stable pairs on nodal fibrations (a gateway to proving Katz-Klemm-Vafa conjecture)
Speaker: Artan Sheshmani, OSU
Seminar Type: Algebraic Geometry, Seminar Website
Abstract: I will talk about joint work with Toda and Gholampour on studying the stable pair theory of K3 fibrations over curves with possibly nodal fibers. We express the stable pair invariants of the fiberwise irreducible classes in terms of the famous Kawai-Yoshioka formula for the Euler characteristics of moduli space of stable pairs on K3 surfaces and Noether-Lefschetz numbers of the fibration. Moreover, we investigate the relation of these invariants to the perverse (non-commutative) stable pair invariants of the K3 fibration. In the case that the K3 fibration is a projective Calabi-Yau threefold, by means of wall-crossing techniques, we write the stable pair invariants of the fiberwise curve classes in terms of the generalized Donaldson-Thomas invariants of 2-dimensional Gieseker semistable sheaves supported on the fibers. Finally if time permits, I will discuss briefly the work in progress, where we use the non-commutative stable pairs theory to prove the famous KKV conjecture.
