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- W2950140989 abstract "Let $X_Sigma$ be a complete toric variety. The coherent-constructible correspondence $kappa$ of cite{FLTZ} equates $Perf_T(X_Sigma)$ with a subcategory $Sh_{cc}(M_bR;LS)$ of constructible sheaves on a vector space $M_bR.$ The microlocalization equivalence $mu$ of cite{NZ,N} relates these sheaves to a subcategory $Fuk(T^*M_bR;LS)$ of the Fukaya category of the cotangent $T^*M_bR$. When $X_Si$ is nonsingular, taking the derived category yields an equivariant version of homological mirror symmetry, $DCoh_T(X_Si)cong DFuk(T^*M_bR;LS)$, which is an equivalence of triangulated tensor categories. The nonequivariant coherent-constructible correspondence $bar{kappa}$ of cite{T} embeds $Perf(X_Si)$ into a subcategory $Sh_c(T_bR^vee;bar{Lambda}_Si)$ of constructible sheaves on a compact torus $T_bR^vee$. When $X_Si$ is nonsingular, the composition of $bar{kappa}$ and microlocalization yields a version of homological mirror symmetry, $DCoh(X_Sigma)hookrightarrow DFuk(T^*T_bR;bar{Lambda}_Si)$, which is a full embedding of triangulated tensor categories. When $X_Si$ is nonsingular and projective, the composition $tau=mucirc kappa$ is compatible with T-duality, in the following sense. An equivariant ample line bundle $cL$ has a hermitian metric invariant under the real torus, whose connection defines a family of flat line bundles over the real torus orbits. This data produces a T-dual Lagrangian brane $mathbb L$ on the universal cover $T^*M_bR$ of the dual real torus fibration. We prove $mathbb Lcong tau(cL)$ in $Fuk(T^*M_bR;LS).$ Thus, equivariant homological mirror symmetry is determined by T-duality." @default.
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- W2950140989 date "2008-11-09" @default.
- W2950140989 modified "2023-09-27" @default.
- W2950140989 title "T-Duality and Equivariant Homological Mirror Symmetry for Toric Varieties" @default.
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