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Holomorphic Lagrangian branes correspond to perverse sheaves. (English) Zbl 1318.53100

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

MSC:

53D40 Symplectic aspects of Floer homology and cohomology
32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects)
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