Some results on fake quadrics
报告专家：杨建强（红河学院）
报告时间：2025年4月11日（星期五）下午16:00-17:00
报告地点：国家天元数学西南中心516
报告摘要：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: \[\mathring{\Eff}(S)=\Amp(S)\subset \SAmp(S)=\Mov(S) \subset \Nef(S)=\Eff(S)=\overline{\Amp(S)}. \] 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 P^1; Subsequently, we show that no fake quadric can be embedded in P^4; Finally, we prove that the fake quadric S possesses the bounded cohomology property. This property is characterized by the existence of a positive constant $c_{S}$ such that $h^1(\CO_S(C))\leq c_S h^0(\CO_S(C))$ for any curve $C \subset S$.
专家简介：杨建强，博士毕业于四川大学数学学院，任职于红河学院，目前在中科院晨兴数学中心和数学研究所访问学，研究方向为代数拓扑与代数几何的交叉领域，特别是对代数簇的分类，代数簇的拓扑性质，有深入的研究。
邀请人：张斌
