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CONSTRUCTING EQUIVARIANT VECTOR BUNDLES VIA THE BGG CORRESPONDENCE

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Abstract

We describe a strategy for the construction of finitely generated G-equivariant Z-graded modules M over the exterior algebra for a finite group G. By an equivariant version of the BGG correspondence, M defines an object F in the bounded derived category of G-equivariant coherent sheaves on projective space. We develop a necessary condition for F being isomorphic to a vector bundle that can be simply read off from the Hilbert series of M. Combining this necessary condition with the computation of finite excerpts of the cohomology table of F makes it possible to enlist a class of equivariant vector bundles on P 4 that we call strongly determined in the case where G is the alternating group on 5 points.
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Dates and versions

hal-01829487 , version 1 (04-07-2018)

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  • HAL Id : hal-01829487 , version 1

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Sébastien Posur. CONSTRUCTING EQUIVARIANT VECTOR BUNDLES VIA THE BGG CORRESPONDENCE. MEGA 2017 - International Conference on Effective Methods in Algebraic Geometry, Jun 2017, Nice, France. ⟨hal-01829487⟩
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