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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Holomorphic Lagrangian branes correspond to perverse sheaves

Xin Jin

Geometry & Topology 19 (2015) 1685–1735
Abstract

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.

Keywords
Fukaya category, holomorphic Lagrangian branes, perverse sheaves, constructible sheaves, Nadler–Zaslow correspondence
Mathematical Subject Classification 2010
Primary: 53D40, 32S60
References
Publication
Received: 29 March 2014
Revised: 18 July 2014
Accepted: 16 August 2014
Published: 21 May 2015
Proposed: Richard Thomas
Seconded: Ciprian Manolescu, Ronald Stern
Authors
Xin Jin
Department of Mathematics
University of California, Berkeley
Berkeley, CA 94720
USA
http://math.berkeley.edu/~xjin/