The asymptotic growth of equivariant sections of positive and big line bundles

2002/07/16 by Roberto Paoletti, Paoletti, Roberto
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.AG #math.SG

paper · pdf · doi:10.48550/arxiv.math/0207128

arxiv created 2002/07/16 · arxiv updated 2009/11/30

Abstract

If a finite group acts holomorphically on a pair (X,L), where X is a complex projective manifold and L a line bundle on it, for every k the space of holomorphic global section of the k-th power of L splits equivariantly according to the irreducible representations of G. We consider the asymptotic growth of these summands, under various positivity conditions on L. The methods apply also to the context of almost complex quantization.

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