Auslander orders over nodal stacky curves and partially wrapped Fukaya categories

By Yankı Lekili, Alexander Polishchuk. Journal of Topology, 2017

49 citations recorded by the source corpus.

It follows from the work of Burban and Drozd [Math. Ann. 351 (2011) 665–709] that for nodal curves C , the derived category of modules over the Auslander order AC provides a categorical (smooth and proper) resolution of the category of perfect complexes Perf (C) . On the A‐side, it follows from the work of Haiden–Katzarkov–Kontsevich [Publ. Math. Inst. Hautes Études Sci. 126 (2017) 247–318] that for punctured surfaces X with stops Λ at their boundary, the partially wrapped Fukaya category W(X,Λ) provides a categorical (smooth and proper) resolution of the compact Fukaya category 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 derived categories of coherent sheaves (respectively perfect complexes) on such nodal stacky curves and the wrapped (respectively compact) Fukaya categories of punctured surfaces of arbitrary genus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a0f0b2780c3a721f76cba512b59c7744cc9b53ae

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In Geometry and Topology

1. Vivek V. Shende
2. J. Pardon
3. Sheel Ganatra
4. Yankı Lekili
5. Alexander Polishchuk
6. Emanuele Macrì
7. Zachary Sylvan
8. Yuri I. Manin

In Mathematical Physics

1. J. Pardon
2. Vivek V. Shende
3. Sheel Ganatra
4. Yankı Lekili
5. Alexander Polishchuk
6. Zachary Sylvan
7. Yuri I. Manin
8. Emanuele Macrì

Citations in the corpus

• A geometric model for the derived category of gentle algebras (2018, unknown): “points on each boundary component and the number of laminates starting and ending on each boundary component (Theorem 6.1). We thus obtain an explicit description of the category Db(A− mod). Based on [46, 53], this category gives a complete instance of homological mirror symmetry (in the trivially g”
• Sectorial descent for wrapped Fukaya categories (2018, background): “) For a generalization of this example to other surfaces, see Lekili–Polishchuk [36].”
• Derived equivalences of gentle algebras via Fukaya categories (2018, methodology): “ived equivalence of finite-dimensional gentle algebras with grading in degree 0 (see Corollary 3.3.1). In a different direction, we construct derived equivalences between stacky nodal curves studied in [21]. Namely, these are either chains or rings of weighted projective lines glued to form stacky nod”