تقرير
Classification of real Riemann surfaces and their Jacobians in the critical case
| العنوان: | Classification of real Riemann surfaces and their Jacobians in the critical case |
|---|---|
| المؤلفون: | Giavedoni, Pietro |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry, Mathematical Physics, Mathematics - Complex Variables, Mathematics - Numerical Analysis |
| الوصف: | For every $g\geq 2$ we distinguish real period matrices of real Riemann surfaces of topological type $(g,0,0)$ from the ones of topological type $(g,k,1)$, with $k$ equal to one or two for $g$ even or odd respectively (Theorem B). To that purpose, we exhibit new invariants of real principally polarized abelian varieties of orthosymmetric type (Theorem A.1). As a direct application, we obtain an exhaustive criterion to decide about the existence of real points on a real Riemann surface, requiring only a real period matrix of its and the evaluation of the sign of at most one (real) theta constant (Theorem C). A part of our real, algebro-geometric instruments first appeared in the framework of nonlinear integrable partial differential equations. Comment: 32 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2307.10486 |
| رقم الأكسشن: | edsarx.2307.10486 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |