In this paper we estimate the minimal number of Darboux charts needed to cover a Hermitian symmetric space of compact type M in terms of the degree of their embeddings in CPN. The proof is based on the recent work of Rudyak and Schlenk (Commun Contemp Math 9(6):811–855, 2007) and on the symplectic geometry tool developed by the first author in collaboration with Loi et al. (J Sympl Geom, 2014). As application we compute this number for a large class of Hermitian symmetric spaces of compact type.
Minimal symplectic atlases of Hermitian symmetric spaces
Mossa R.;Placini G.
2015-01-01
Abstract
In this paper we estimate the minimal number of Darboux charts needed to cover a Hermitian symmetric space of compact type M in terms of the degree of their embeddings in CPN. The proof is based on the recent work of Rudyak and Schlenk (Commun Contemp Math 9(6):811–855, 2007) and on the symplectic geometry tool developed by the first author in collaboration with Loi et al. (J Sympl Geom, 2014). As application we compute this number for a large class of Hermitian symmetric spaces of compact type.
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