论文标题
光滑完整交叉口的扭曲对称能力的扭曲对称能力的共同学
Cohomology of twisted symmetric powers of cotangent bundles of smooth complete intersections
论文作者
论文摘要
在本文中，我们提供了两种不同的分辨率，这些分辨率是平滑完整交叉点的项目活动切线束的结构或骨。这些决议尤其允许获得方便（完全明确的）描述，这些共同体的扭曲对称能力的共同捆绑包的共同捆绑包的完整交叉点，这些交叉点很容易在计算机上实现。然后，我们提供多个应用程序。首先，我们在该主题上恢复了已知的消失定理，并证明它们是通过一些非变化定理的最佳选择。然后，我们研究了$ω_x（1）$的对称能力的全球部分的对称代数，其中$ x $是平滑的完整完整的codimension $ c <n/2 $，改善了文献中已知的结果。我们还研究了一般性超曲面的副束的部分扩张。最后，我们说明了如何在计算机上实现同事的明确描述。特别是，这允许展示新的和简单的表面家族示例，沿着规范扭曲的Pluri-Genera不会保持恒定。
In this paper, we provide two different resolutions of structural sheaves of projectivized tangent bundles of smooth complete intersections. These resolutions allow in particular to obtain convenient (and completely explicit) descriptions of cohomology of twisted symmetric powers of cotangent bundles of complete intersections, which are easily implemented on computer. We then provide several applications. First, we recover the known vanishing theorems on the subject, and show that they are optimal via some non-vanishing theorems. Then, we study the symmetric algebra of global sections of symmetric powers of $Ω_X(1)$, where $X$ is a smooth complete intersection of codimension $c < N/2$, improving the known results in the literature. We also study partial ampleness of cotangent bundles of general hypersurfaces. Finally, we illustrate how the explicit descriptions of cohomology can be implemented on computer. In particular, this allows to exhibit new and simple examples of family of surfaces along which the canonically twisted pluri-genera do not remain constant.
