Report
On the existence of logarithmic and orbifold jet differentials
| العنوان: | On the existence of logarithmic and orbifold jet differentials |
|---|---|
| المؤلفون: | Campana, Frédéric, Darondeau, Lionel, Demailly, Jean-Pierre, Rousseau, Erwan |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry, 32Q45, 32H30, 14F06 |
| الوصف: | 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. Comment: 56 pages, version 2 corrects minor typos and adds a few lines of explanation in the introduction |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2109.00764 |
| رقم الانضمام: | edsarx.2109.00764 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |