数学研究所
学术报告
代数几何研讨班
Speaker: 杨建强 副教授 （红河学院）
Title: Some results on fake quadrics
Time&Venue: 2025.4.15（周二）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.