Holomorphic Lagrangian branes correspond to perverse sheaves

Jin, Xin

doi:10.2140/gt.2015.19.1685

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Holomorphic Lagrangian branes correspond to perverse sheaves

Xin Jin

Geometry & Topology 19 (2015) 1685–1735

DOI: 10.2140/gt.2015.19.1685

Abstract

Let $X$ be a compact complex manifold, $D_{c}^{b} (X)$ be the bounded derived category of constructible sheaves on $X$ , and $Fuk (T^{*} X)$ be the Fukaya category of $T^{*} X$ . A Lagrangian brane in $Fuk (T^{*} X)$ is holomorphic if the underlying Lagrangian submanifold is complex analytic in $T^{*} X_{ℂ}$ , the holomorphic cotangent bundle of $X$ . We prove that under the quasiequivalence between $D_{c}^{b} (X)$ and $DFuk (T^{*} X)$ 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/

Volume 19, issue 3 (2015)