تقرير
Complex surfaces with many algebraic structures
| العنوان: | Complex surfaces with many algebraic structures |
|---|---|
| المؤلفون: | Abasheva, Anna, Déev, Rodion |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Complex Variables, Mathematics - Algebraic Geometry, Mathematics - K-Theory and Homology, 32J05 (Primary) 14J26, 19E99, 32Q40, 14H52 (Secondary) |
| الوصف: | We find new examples of complex surfaces with countably many non-isomorphic algebraic structures. Here is one such example: take an elliptic curve $E$ in $\mathbb P^2$ and blow up nine general points on $E$. Then the complement $M$ of the strict transform of $E$ in the blow-up has countably many algebraic structures. Moreover, each algebraic structure comes from an embedding of $M$ into a blow-up of $\mathbb P^2$ in nine points lying on an elliptic curve $F\not\simeq E$. We classify algebraic structures on $M$ using a Hopf transform: a way of constructing a new surface by cutting out an elliptic curve and pasting a different one. Next, we introduce the notion of an analytic K-theory of varieties. Manipulations with the example above lead us to prove that classes of all elliptic curves in this K-theory coincide. To put in another way, all motivic measures on complex algebraic varieties that take equal values on biholomorphic varieties do not distinguish elliptic curves. Comment: 18 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2303.10764 |
| رقم الأكسشن: | edsarx.2303.10764 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |