HMS for punctured tori and categorical mapping class group actions

2011/11/22 by Nicolò Sibilla, Nicolo` Sibilla, Sibilla, Nicolo` · 1 citation
Mathematics · #53D02 #53D37 #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.AG #math.GT #math.SG #msc:53D02 #msc:53D37

paper · pdf · doi:10.48550/arxiv.1111.5284

10 pages. To appear in Proceedings of the String-Math 2011 conference

arxiv created 2011/11/22 · openalex publication_date 2011/11/22 · arxiv updated 2011/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X_n be a cycle of n projective lines, and T_n a symplectic torus with n punctures. In this paper we review results appeared in arXiv:1103.2462 and in arXiv:1109.6615, which establish a version of homological mirror symmetry relating X_n and T_n, and define on D^b(Coh(X_n)) an action of the pure mapping class group of T_n.

Citations

• Ribbon Graphs and Mirror Symmetry I
• A note on mapping class group actions on derived categories

Cited by

• Mirror Symmetry in dimension one and Fourier-Mukai equivalences

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• A note on mapping class group actions on derived categories
• Hypergeometric functions and mirror symmetry in toric varieties
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