تقرير
Hermitian Yang-Mills functionals on direct images
| العنوان: | Hermitian Yang-Mills functionals on direct images |
|---|---|
| المؤلفون: | Finski, Siarhei |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Differential Geometry, Mathematics - Algebraic Geometry, Mathematics - Complex Variables, 53C07, 32Q26, 14D06, 58E15 |
| الوصف: | For a polarized family of complex projective manifolds, we study the Hermitian Yang-Mills functionals on the sequence of vector bundles over the base of the family associated with direct image sheaves of the tensor powers of the polarization. We make a connection between the asymptotic minimization of these functionals, for big tensor powers of the polarization, and the minimization of the so-called Wess-Zumino-Witten functional defined on the space of all relatively K\"ahler $(1, 1)$-forms on the fibration. We establish the sharp lower bounds on the latter functional in terms of the limiting Harder-Narasimhan measure, which is a certain algebraic invariant of the family. As an application, in a fibered setting, we prove an asymptotic converse to the Andreotti-Grauert theorem conjectured by Demailly. Comment: 45 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.06034 |
| رقم الأكسشن: | edsarx.2407.06034 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |