Holomorphic Lagrangian branes correspond to perverse sheaves
Holomorphic Lagrangian branes correspond to perverse sheaves
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全纯拉格朗日膜对应于反常滑轮
DOI：
10.2140/gt.2015.19.1685
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发表时间：
2013
影响因子：
2
通讯作者：
Xin Jin
中科院分区：
文献类型：
--
作者：
Xin Jin
设X是紧致复流形，$D_c^B（X）$是X$上可构造层的有界导范畴，$Fuk（T^*X）$是T^*X$的福谷范畴.一个在$Fuk（T^*X）$中的拉格朗日膜是全纯的，如果其下的拉格朗日子流形在$T^*X_{\mathbb{C}}$中是复解析的，$X$的全纯余切丛。证明了在[NaZa 09]和[Nad 09]中建立的$D^B_c（X）$和$DFuk（T^*X）$之间的拟等价性下，具有适当阶化的全纯拉格朗日膜对应于反常层.
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 $T^*X_{\mathbb{C}}$, the holomorphic cotangent bundle of $X$. We prove that under the quasi-equivalence between $D^b_c(X)$ and $DFuk(T^*X)$ established in [NaZa09] and [Nad09], holomorphic Lagrangian branes with appropriate grading correspond to perverse sheaves.