文献类型：期刊文献

英文题名：Bounded cohomology property on a smooth projective surface with Picard number two

作者：Li, Sichen[1,2]

机构：[1]East China Univ Sci & Technol, Sch Math, Shanghai, Peoples R China;[2]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China

年份：2023

卷号：51

期号：12

起止页码：5235

外文期刊名：COMMUNICATIONS IN ALGEBRA

收录：;WOS:【SCI-EXPANDED(收录号:WOS:001020437400001)】；

语种：英文

外文关键词：Bounded cohomology property; bounded negativity conjecture; Picard number two; Primary: 14C20

摘要：We say a smooth projective surface $X$ satisfies the bounded cohomology property if there exists a positive constant $c_X$ such that $h<^>1(mathcal O_X(C))le c_Xh<^>0(mathcal O_X(C))$ for every prime divisor $C$ on $X$. Let the closed Mori cone $mathrm{NE}(X)=mathbb R_{ge0}[C_1]+mathbb R_{ge0}[C_2]$ such that $C_1$ and $C_2$ with $C_2<^>2<0$ are some curves on $X$. If either (i) the Kodaira dimension $kappa(X)le1$ or (ii) $kappa(X)=2$, the irregularity $q(X)=0$ and the Iitaka dimension $kappa(X,C_1)=1$, then we prove that $X$ satisfies the bounded cohomology property.