关于对数和轨道射流微分的存在性
On the existence of logarithmic and orbifold jet differentials
摘要：
引入了有向轨道的概念，即由有向代数簇或解析簇（X，V）和一个分歧因子D构成的三元组（X，V，D），其中V是切丛TX的凝聚子层.在这方面，我们介绍了一个代数的orbifold喷流微分和他们的部分。这些喷流截面可以看作是作用在具有亚纯系数的曲线芽上的代数微分算子，其极点由D支撑，重数由D的分支的分歧指数限定。我们精确地估计曲率张量的相应的有向结构V[D]在一般的orbifold的情况下，特别注意到紧凑的情况D = 0和对数的情况下，分歧指数是无限的。利用投射化的轨道Green-Griffiths丛的重言线丛上的全纯Morse不等式，得到了整体轨道喷流微分存在的有效充分条件.
英文摘要：
We introduce the concept of directed orbifold, namely triples (X, V, D) formed by a directed algebraic or analytic variety (X, V), and a ramification divisor D, where V is a coherent subsheaf of the tangent bundle TX. In this context, we introduce an algebra of orbifold jet differentials and their sections. These jet sections can be seen as algebraic differential operators acting on germs of curves, with meromorphic coefficients, whose poles are supported by D and multiplicities are bounded by the ramification indices of the components of D. We estimate precisely the curvature tensor of the corresponding directed structure V[D] in the general orbifold case-with a special attention to the compact case D = 0 and to the logarithmic situation where the ramification indices are infinite. Using holomorphic Morse inequalities on the tautological line bundle of the projectivized orbifold Green-Griffiths bundle, we finally obtain effective sufficient conditions for the existence of global orbifold jet differentials.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
