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Is the following statement well known? Let $M,N$ be symplectic (algebraic) manifolds. Let $L \subset M \times N$ be a (smooth) Lagrangian correspondence. For a subset $X \subset M$ we denote $L(X):={y\in L(X):=(y\in N|(x,y)\in L}$L)$. Let $X \subset M$ be an isotropic subvariety (i.e. its smooth locus is isotropic). Then $L(X)$ is isotropic. Is it written somewhere? I think I can prove it and it is quite simple, but I'll rather use a reference instead. Thank you |
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Image of an isotropic manifold under lagrangian correspondence is isotropic?Is the following statement well known? Let $M,N$ be symplectic (algebraic) manifolds. Let $L \subset M \times N$ be a (smooth) Lagrangian correspondence. For a subset $X \subset M$ we denote $L(X):={y\in N|(x,y)\in L}$. Let $X \subset M$ be an isotropic subvariety (i.e. its smooth locus is isotropic). Then $L(X)$ is isotropic. Is it written somewhere? I think I can prove it and it is quite simple, but I'll rather use a reference instead. Thank you
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