Symplectic log Kodaira dimension -∞, affine-ruledness and unicuspidal rational curves
Prof. Tianjun Li
2025-06-09 16:00-17:00
MCM610
Speaker: Prof. Tianjun Li (University of Minnesota)
Time: 16:00-17:00 June 9, 2025 (Monday)
Venue: MCM610
Title: Symplectic log Kodaira dimension -∞, affine-ruledness and unicuspidal rational curves
Abstract: A classical theorem of Liu-Ohta-Ono asserts that any symplectic 4-manifold with negative pairing between the symplectic form and canonical class must be rational or ruled. This result is a symplectic reminiscence of the more classical characterization of complex surfaces with Kodaira dimension -∞. In this talk, we will discuss the generalization of Liu-Ohta-Ono's theorem to the relative setting by considering symplectic divisors whose adjoint class has negative pairing with canonical class. In parallel to the theorem of Fujita-Miyanishi-Sugie-Russell in the algebraic context, we show that the complement of such divisors is foliated by a certain family of unicuspidal rational curves, thereby admitting the affine-ruled structure. This is based on joint work with Shengzhen Ning.
