Holomorphic Lagrangian branes correspond to perverse sheaves

Jin, Xin¹

¹ Department of Mathematics, University of California, Berkeley, Berkeley, CA 94720, USA

Geometry & topology, Tome 19 (2015) no. 3, pp. 1685-1735.

Résumé

Let $X$ be a compact complex manifold, $D_c^b\left(X\right)$ be the bounded derived category of constructible sheaves on $X$, and $Fuk\left(T^{\ast }X\right)$ be the Fukaya category of $T^{\ast }X$. A Lagrangian brane in $Fuk\left(T^{\ast }X\right)$ is holomorphic if the underlying Lagrangian submanifold is complex analytic in $T^{\ast }{X}_{ℂ}$, the holomorphic cotangent bundle of $X$. We prove that under the quasiequivalence between $D_c^b\left(X\right)$ and $DFuk\left(T^{\ast }X\right)$ established by Nadler and Zaslow, holomorphic Lagrangian branes with appropriate grading correspond to perverse sheaves.

Détail

DOI : 10.2140/gt.2015.19.1685

Classification : 53D40, 32S60
Keywords: Fukaya category, holomorphic Lagrangian branes, perverse sheaves, constructible sheaves, Nadler–Zaslow correspondence

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