تقرير
Ungraded matrix factorizations as mirrors of non-orientable Lagrangians
| العنوان: | Ungraded matrix factorizations as mirrors of non-orientable Lagrangians |
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| المؤلفون: | Amorim, Lino, Cho, Cheol-Hyun |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Symplectic Geometry, Mathematical Physics, Mathematics - Algebraic Geometry |
| الوصف: | We introduce the notion of ungraded matrix factorization as a mirror of non-orientable Lagrangian submanifolds. An ungraded matrix factorization of a polynomial $W$, with coefficients in a field of characteristic 2, is a square matrix $Q$ of polynomial entries satisfying $Q^2 = W \cdot \mathrm{Id}$. We then show that non-orientable Lagrangians correspond to ungraded matrix factorizations under the localized mirror functor and illustrate this construction in a few instances. Our main example is the Lagrangian submanifold $\mathbb{R}P^2 \subset \mathbb{C}P^2$ and its mirror ungraded matrix factorization, which we construct and study. In particular, we prove a version of Homological Mirror Symmetry in this setting. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2205.01046 |
| رقم الأكسشن: | edsarx.2205.01046 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |