تقرير
Degenerations and Fibrations of K3 Surfaces: Lattice Polarisations and Mirror Symmetry
| العنوان: | Degenerations and Fibrations of K3 Surfaces: Lattice Polarisations and Mirror Symmetry |
|---|---|
| المؤلفون: | Giovenzana, Luca, Thompson, Alan |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry, 14D06, 14J28 (14J26, 14J27, 14J33, 53D37) |
| الوصف: | Tyurin degenerations of K3 surfaces are degenerations whose central fibre consists of a pair of rational surfaces glued along a smooth elliptic curve. We study the lattice theory of such Tyurin degenerations, establishing a notion of lattice polarisation that is compatible with existing definitions for the general fibre and the rational surfaces comprising the central fibre. We separately consider elliptically fibred K3 surfaces, where the base of the fibration admits a splitting into a pair of discs with specified monodromy around the boundary. In this setting we establish a notion of lattice polarisation for the induced elliptic fibrations over discs, which is compatible with the existing definition for K3 surfaces. Finally, we discuss the mirror symmetric correspondence between these two settings. Comment: v3: Prop 2.37 has been strengthened to remove the degree nonzero assumption. This has allowed a simplification of Def 5.1: the new definition is equivalent but easier to work with. The former Prop 5.3 is no longer needed and has been removed, and the former Prop 5.4 (now 5.3) has been simplified. Various other minor corrections and clarifications |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2405.12009 |
| رقم الأكسشن: | edsarx.2405.12009 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |