Speaker: 杨建强副教授，红河学院

Inviter: 陈亦飞副研究员

Title: Some results on fake quadrics

Language: Chinese

Time & Venue: 2025.04.15 10:00-11:30 晨兴410

Abstract: In this talk, we give a criterion to assess the effectiveness and ampleness of divisors on a fake quadric surface S, and then we establish a relationship between the cones:Int Eff(S)=Amp(S) \subset SAmp(S)=Mov(S) \subset Nef(S)=Eff(S)=\overline{Amp(S)}.In particular, we prove that any fake quadric of odd type does not contain a negative curve. This result is central to our manuscript.As applications, first, we give that any fake quadric is a fibration over P1. Subsequently, we show that no fake quadric can be embedded in P4. Finally, we prove that the fake quadric S possesses the bounded cohomology property. This property is characterized by the existence of a positive constant cS such that h1(OS(C))≤cS h0(OS(C)) for any curve C in S.