تقرير
A generalized Schmidt subspace theorem for closed subschemes
| العنوان: | A generalized Schmidt subspace theorem for closed subschemes |
|---|---|
| المؤلفون: | Heier, Gordon, Levin, Aaron |
| سنة النشر: | 2017 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, Mathematics - Algebraic Geometry, Mathematics - Complex Variables, 11J87, 11G35, 11G50, 14C20, 14E05, 14G40, 32H30 |
| الوصف: | We prove a generalized version of Schmidt's subspace theorem for closed subschemes in general position in terms of suitably defined Seshadri constants with respect to a fixed ample divisor. Our proof builds on previous work by Evertse and Ferretti, Corvaja and Zannier, and others, and uses standard techniques from algebraic geometry such as notions of positivity, blowing-ups and direct image sheaves. As an application, we recover a higher-dimensional Diophantine approximation theorem of K.F. Roth-type due to D. McKinnon and M. Roth with a significantly shortened proof, while simultaneously extending the scope of the use of Seshadri constants in this context in a natural way. Comment: Added more details to the proof of the main theorem. Added Section 4, giving new results comparing beta constants and Seshadri constants for closed subschemes. Fixed minor typos and updated the bibliography |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1712.02456 |
| رقم الأكسشن: | edsarx.1712.02456 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |