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
本文针对皮卡数为2的光滑射影曲面，刻画满足有界上同调性质的曲面，明确了该性质的核心不等式条件，为相关代数几何研究提供了具体刻画方法。
AI 中文摘要
设X为皮卡数为2的光滑射影曲面，X要么是几何直纹曲面，要么闭Mori锥是有理多面体。本文刻画具有有界上同调性质的X，即存在常数c_X>0，使得对X上任意曲线C，有h^1(𝒪_X(C))≤c_X h^0(𝒪_X(C))成立。
英文摘要
Let $X$ be a smooth projective surface with Picard number two, where either $X$ is a geometrically ruled surface or the closed Mori cone is rational polyhedral. In this paper, we characterize $X$ with the bounded cohomology property, i.e., there exists a constant $c_X>0$ such that $h^1(\mathcal O_X(C))\le c_Xh^0(\mathcal O_X(C))$ for every curve $C$ on $X$.
Comments11 pages, accepted by Geom. Dedicata, comments are welcome!
