Open Access
2015 Holomorphic Lagrangian branes correspond to perverse sheaves
Xin Jin
Geom. Topol. 19(3): 1685-1735 (2015). DOI: 10.2140/gt.2015.19.1685


Let X be a compact complex manifold, Dcb(X) be the bounded derived category of constructible sheaves on X, and Fuk(TX) be the Fukaya category of TX. A Lagrangian brane in Fuk(TX) is holomorphic if the underlying Lagrangian submanifold is complex analytic in TX, the holomorphic cotangent bundle of X. We prove that under the quasiequivalence between Dcb(X) and DFuk(TX) established by Nadler and Zaslow, holomorphic Lagrangian branes with appropriate grading correspond to perverse sheaves.


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Xin Jin. "Holomorphic Lagrangian branes correspond to perverse sheaves." Geom. Topol. 19 (3) 1685 - 1735, 2015.


Received: 29 March 2014; Revised: 18 July 2014; Accepted: 16 August 2014; Published: 2015
First available in Project Euclid: 16 November 2017

zbMATH: 1318.53100
MathSciNet: MR3352247
Digital Object Identifier: 10.2140/gt.2015.19.1685

Primary: 32S60 , 53D40

Keywords: constructible sheaves , Fukaya category , holomorphic Lagrangian branes , Nadler–Zaslow correspondence , perverse sheaves

Rights: Copyright © 2015 Mathematical Sciences Publishers

Vol.19 • No. 3 • 2015
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