تقرير
On a B-field transform of generalized complex structures over complex tori
| العنوان: | On a B-field transform of generalized complex structures over complex tori |
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| المؤلفون: | Kobayashi, Kazushi |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics High Energy Physics - Theory |
| مصطلحات موضوعية: | Mathematics - Differential Geometry, High Energy Physics - Theory, 14J33, 53D37, 53D18, 14F08, 53C08 |
| الوصف: | Let $(X^n,\check{X}^n)$ be a mirror pair of an $n$-dimensional complex torus $X^n$ and its mirror partner $\check{X}^n$. Then, by SYZ transform, we can construct a holomorphic line bundle with an integrable connection from each pair of a Lagrangian section of $\check{X}^n\to \mathbb{R}^n/\mathbb{Z}^n$ and a unitary local system along it, and those holomorphic line bundles with integrable connections forms a dg-category $DG_{X^n}$. In this paper, we focus on a certain B-field transform of the generalized complex structure induced from the complex structure on $X^n$, and interpret it as the deformation $X_{\mathcal{G}}^n$ of $X^n$ by a flat gerbe $\mathcal{G}$. Moreover, we construct the deformation of $DG_{X^n}$ associated to the deformation from $X^n$ to $X_{\mathcal{G}}^n$, and also discuss the homological mirror symmetry between $X_{\mathcal{G}}^n$ and its mirror partner on the object level. Comment: 38 pages. arXiv admin note: substantial text overlap with arXiv:2209.15160 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2403.15515 |
| رقم الأكسشن: | edsarx.2403.15515 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |