The category of perverse sheaves on smooth toric varieties
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Thu, 16/06/2011 14:30 |
Delphine Dupont (Oxford) |
Representation Theory Seminar  |
L3 |
| The category of perverse sheaves, Perv_X, on a stratified space X plays an important role in the Intersection cohomology of Goresky-MacPherson and on the theory of D-modules. It is defined as a subcategory of the derived category of sheaves. Hence a usual complaint is that there are not very concrete objects. A lot of work has been done to describe Perv_X more explicitly. Hence many methods had been develop to describe Perv_X as a category of quiver representations. An important property of perverse sheaves is that they can be viewed as a stack, it means that a perverse sheaf can be defined up to isomorphism from the data of perverse sheaves on an open cover of X plus some glueing data. In this talk we show how the theory of stacks and more precisely the notion of constructible stacks can be used in order to glue a description due to Galligo, Granger and Maisonobe of the category Perv_X when X is C^n stratified by a normal crossing stratification. Thanks to this we will obtain a description of Perv_X on smooth toric varieties stratified by the torus action. | |||