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Auslander orders over nodal stacky curves and partially wrapped Fukaya categories. (arXiv:1705.06023v1 [math.SG])
来源于:arXiv
It follows from the work of Burban and Drozd arXiv:0905.1231 that for nodal
curves $C$, the derived category of modules over the Auslander order
$\mathcal{A}_C$ provides a categorical (smooth and proper) resolution of the
category of perfect complexes $\mathrm{Perf}(C)$. On the A-side, it follows
from the work of Haiden-Katzarkov-Kontsevich arXiv:1409.8611 that for punctured
surfaces $X$ with stops $\Lambda$ at their boundary, the partially wrapped
Fukaya category $\mathcal{W}(X,\Lambda)$ provides a categorical (smooth and
proper) resolution of the compact Fukaya category $\mathcal{F}(X)$. Inspired by
this analogy, we establish an equivalence between the derived category of
modules over the Auslander orders over certain nodal stacky curves and
partially wrapped Fukaya categories associated to punctured surfaces of
arbitrary genus equipped with stops at their boundary. As an application, we
deduce equivalences between perfect derived categories of coherent sheaves on
such nodal stacky c 查看全文>>