发表机构
School of Mathematics, East China University of Science and Technology（华东理工大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对特定雅可比椭圆曲面，证明其Mori锥为单纯的，进而推导其满足有界上同调性质，还给出满足对应条件的极小光滑射影曲面的BCP充要条件。
AI 中文摘要
设X为具有有限Mordell-Weil群且恰有一个可约纤维的雅可比椭圆曲面。我们证明，若χ(𝒪_X)≥ρ(X)，则X的Mori锥是单纯的。作为应用，在额外假设q(X)=0的前提下，我们证明X满足有界上同调性质（BCP）：存在常数c_X>0，使得对X上的任意曲线C，均有h¹(𝒪_X(C))≤c_X h⁰(𝒪_X(C))。我们还建立了极小光滑射影曲面Y满足BCP的充要条件，其中Y满足κ(Y)≥1、q(Y)=0且具有有理多面体Mori锥。
英文摘要
Let $X$ be a Jacobian elliptic surface with finite Mordell-Weil group and exactly one reducible fiber. We prove that if $χ(\mathcal O_X)\ge ρ(X)$, then the Mori cone of $X$ is simplicial. As an application, assuming additionally $q(X)=0$, we show that $X$ satisfies the bounded cohomology property (BCP): there exists a constant $c_X>0$ such that $h^1(\mathcal O_X(C))\le c_X h^0(\mathcal O_X(C))$ for every curve $C$ on $X$. We also establish a necessary and sufficient condition for the BCP to hold on minimal smooth projective surfaces $Y$ with $κ(Y)\ge 1$, $q(Y)=0$, and rational polyhedral Mori cones.
Comments11 pages, comments are welcome!
