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CONSTRUCTION OF EQUIVARIANT VECTOR BUNDLES

Michel Brion

Open publisher page 3 citations

Abstract

Abstract. Let X be the wonderful compactification of a complex adjoint symmetric space G/K such that rk(G/K) = rk(G) − rk(K). We show how to extend equivariant vector bundles on G/K to equivariant vector bundles on X, generated by their global sections and having trivial higher cohomology groups. This relies on a geometric construction of equivariant vector bundles in the setting of varieties with reductive group action and “multiplicity-free ” subvarieties.

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What this paper is about

Abstract. Let X be the wonderful compactification of a complex adjoint symmetric space G/K such that rk(G/K) = rk(G) − rk(K). We show how to extend equivariant vector bundles on G/K to equivariant vector bundles on X, generated by their global sections and having trivial higher cohomology groups. This relies on a geometric construction of equivariant vector bundles in the setting of varieties with reductive group action and “multiplicity-free ” subvarieties.

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Available abstract

Abstract. Let X be the wonderful compactification of a complex adjoint symmetric space G/K such that rk(G/K) = rk(G) − rk(K). We show how to extend equivariant vector bundles on G/K to equivariant vector bundles on X, generated by their global sections and having trivial higher cohomology groups. This relies on a geometric construction of equivariant vector bundles in the setting of varieties with reductive group action and “multiplicity-free ” subvarieties.

Key concepts: Equivariant map, Vector bundle, Computer science, Pure mathematics, Mathematics

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