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Equivariant vector bundles on complete symmetric varieties of minimal rank

Indranil Biswas

School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 500004, India

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S. Senthamarai Kannan

Chennai Mathematical Institute, Plot H1, Sipcot IT Park, Siruseri, Kelambakam, Chennai 603103, India

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, and

D. S. Nagaraj

Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India

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https://doi.org/10.1142/S0129167X14501201Cited by:2 (Source: Crossref)

Abstract

Let X be the wonderful compactification of a complex symmetric space G/H of minimal rank. For a point x ∈ G, denote by Z the closure of BxH/H in X, where B is a Borel subgroup of G. The universal cover of G is denoted by . Given a equivariant vector bundle E on X, we prove that E is nef (respectively, ample) if and only if its restriction to Z is nef (respectively, ample). Similarly, E is trivial if and only if its restriction to Z is so.

Keywords:

AMSC: 14F17

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