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Almost holomorphic embeddings in Grassmannians with applications to singular symplectic submanifolds

Muñoz, Vicente and Presas , Francisco and Sols Lucía, Ignacio (2002) Almost holomorphic embeddings in Grassmannians with applications to singular symplectic submanifolds. Journal fur die Reine und Angewandte Mathematik, 547 . pp. 149-189. ISSN 0075-4102

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Abstract

In this paper we use Donaldson's approximately holomorphic techniques to build embeddings of a closed symplectic manifold with symplectic form of integer class in the Grassmannians Gr(r, N). We assure that these embeddings are asymptotically holomorphic in a precise sense. We study first the particular case of CPN obtaining control on N and we improve in a sense a classical result about symplectic embeddings. The main reason of our Study is the construction of singular determinantal submanifolds as the intersection of the embedding with certain "generalized Schubert cycles" defined on a product of Grassmannians. It is shown that the symplectic type of these submanifolds is quite more general that the ones obtained by Donaldson and Auroux,as zeroes of "very ample" vector bundles.


Item Type:Article
Uncontrolled Keywords:Grassmannians; Symplectic manifold; Compatible almost complex structure
Subjects:Sciences > Mathematics > Differential geometry
Sciences > Mathematics > Geometry
ID Code:17153
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Deposited On:20 Nov 2012 12:49
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