报告题目 (Title):有效正交性定理 (Effective Gonality Theorem)
报告人 (Speaker):牛文博 教授(美国阿肯色大学)
报告时间 (Time): 2025年6月10日 (周二) 15:40-16:40
报告地点 (Place):校本部 GJ303
邀请人(Inviter): 毛雪峰
报告摘要:在这一讲中,我将讨论有效正交性定理。1986年,Green-Lazarsfeld提出了gonality猜想,认为光滑投影曲线的gonality可以从曲线上一个足够正的线束的权一合集中得到。他们还提出了这种线束可能存在的最小程度。2015年,Ein-Lazarsfeld证明了足够大度线束的猜想,但该猜想的有效部分仍然广泛开放,并由Farkas-Kemeny重新明确表述。在本文中,我们建立了权一合子的有效消失定理,它蕴涵了有效的正交性猜想。这项研究是与Jinhyung Park一起合作取得的。
Abstract:In this talk, I will discuss effective result for gonality theorem. In 1986, Green-Lazarsfeld raised the gonality conjecture asserting that the gonality of a smooth projective curve can be read off from weight-one syzygies of a sufficiently positive line bundle on the curve. They also proposed possible least degree of such a line bundle. In 2015, Ein--Lazarsfeld proved the conjecture for line bundles of sufficiently large degree, but the effective part of the conjecture remained widely open and was reformulated explicitly by Farkas-Kemeny. In this talk, we establish an effective vanishing theorem for weight-one syzygies, which implies the effective gonality conjecture. This is a joint work with Jinhyung Park.