论文标题
Del Pezzo表面和$ D $ -Simplicity的切线束的束缚
Bigness of the tangent bundle of del Pezzo surfaces and $D$-simplicity
论文作者
论文摘要
我们考虑了在其差异操作员$ d_r $的戒指的动作下，环$ r $简单的问题。我们举例说明，即使$ r $是Gorenstein，并且具有合理的颗粒性$ r $也不是一个简单的$ d_r $ -module；例如，当$ r $是光滑立方表面的均匀坐标环时，情况就是这种情况。我们的示例是平滑的Fano品种的均匀坐标环，我们的证明是通过证明这种品种的切线不必大的束缚。我们还给出了部分逆向，表明当$ r $是平滑投影型品种$ x $的均质坐标环，由其规范的某个规范除数嵌入，然后$ r $的简单性作为$ d_r $ -mmodule，意味着$ x $是fano is fano，因此$ r $ $ r $具有理性的象征。
We consider the question of simplicity of a ring $R$ under the action of its ring of differential operators $D_R$. We give examples to show that even when $R$ is Gorenstein and has rational singularities $R$ need not be a simple $D_R$-module; for example, this is the case when $R$ is the homogeneous coordinate ring of a smooth cubic surface. Our examples are homogeneous coordinate rings of smooth Fano varieties, and our proof proceeds by showing that the tangent bundle of such a variety need not be big. We also give a partial converse showing that when $R$ is the homogeneous coordinate ring of a smooth projective variety $X$, embedded by some multiple of its canonical divisor, then simplicity of $R$ as a $D_R$-module implies that $X$ is Fano and thus $R$ has rational singularities.
