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Exact functors on perverse coherent sheaves
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Inspired by symplectic geometry and a microlocal characterizations of perverse (constructible) sheaves we consider an alternative definition of perverse coherent sheaves. We show that a coherent sheaf is perverse if and only if
$R{\rm\Gamma}_{Z}{\mathcal{F}}$
is concentrated in degree
$0$
for special subvarieties
$Z$
of
$X$
. These subvarieties
$Z$
are analogs of Lagrangians in the symplectic case.
Title: Exact functors on perverse coherent sheaves
Description:
Inspired by symplectic geometry and a microlocal characterizations of perverse (constructible) sheaves we consider an alternative definition of perverse coherent sheaves.
We show that a coherent sheaf is perverse if and only if
$R{\rm\Gamma}_{Z}{\mathcal{F}}$
is concentrated in degree
$0$
for special subvarieties
$Z$
of
$X$
.
These subvarieties
$Z$
are analogs of Lagrangians in the symplectic case.
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