57 research outputs found
Remarks on the nonequivariant coherent-constructible correspondence for toric varieties
We prove the following result of Bondal's: that there is a fully faithful
embedding of the perfect derived category of a proper toric variety
into the derived category of constructible sheaves on a compact torus. We
compare this result to a torus-equivariant version considered in joint work
with Fang, Liu, and Zaslow. There we showed that in the torus-equivariant
version the image of the embedding is cut out by microlocal conditions. To
establish a similar characterization of the image of is an open
problem
Brane structures in microlocal sheaf theory
Let be an exact Lagrangian submanifold of a cotangent bundle ,
asymptotic to a Legendrian submanifold . We study
a locally constant sheaf of -categories on , called the sheaf of
brane structures or . Its fiber is the -category of
spectra, and we construct a Hamiltonian invariant, fully faithful functor from
to the -category of sheaves of spectra on
with singular support in .Comment: 35 pages, 13 figure
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