Leray’s quantization of projective duality

D'Agnolo, Andrea; Schapira, Pierre

doi:10.1215/s0012-7094-96-08415-x

Cited by 32 publications

(9 citation statements)

References 15 publications

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“…The sheaf ρ −1 ν sa χ O w X is concentrated in degree zero. This follows from the following result of [4,5]…”

Section: We Denote By O Wmentioning

confidence: 78%

Multi-specialization and multi-asymptotic expansions

Honda¹,

Prelli²

2011

Proc. Japan Acad. Ser. A Math. Sci.

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In this paper we extend the notion of specialization functor to the case of several closed submanifolds satisfying some suitable conditions. Applying this functor to the sheaf of Whitney holomorphic functions we construct different kinds of sheaves of multi-asymptotically developable functions, whose definitions are natural extensions of the definition of strongly asymptotically developable functions introduced by Majima. Contents1 Multi-normal deformation 5 2 Multi-actions 13 3 Multi-cones 15 4 Multi-normal cones 16 5 Morphisms between multi-normal deformations 24 6 Multi-specialization 33 7 Multi-asymptotic expansions 40 8 Multi-specialization and asymptotic expansions 59 A Conic sheaves 67 B Multi-conic sheaves 69 C Multi-actions in R n 72 D Proof of Proposition 4.7 76References 89Namely, we need the notion of multi-normal deformation and the one of multi-specialization introduced in this paper, which are our main subjects. Let us briefly explain these new notions. Let X be a n-dimensional real analytic manifold with dim X = n, and let χ = {M 1 , . . . , M ℓ } be a family of connected closed submanifolds satisfying some suitable conditions. The multi-normal deformation of X with respect to χ is constructed as follows. We first construct the normal deformation X M 1 of X along M 1 defined by M. Kashiwara and P. Schapira in [10]. Then, taking the pull-back of M 2 in X M 1 , we can obtain the normal deformation X M 1 ,M 2 of X M 1 along the pull-back of M 2 . Then we can define recursively the normal deformation along χ as X = X M 1 ,...,M ℓ :. This manifold is of dimension n + ℓ, it is locally isomorphic to X × R ℓ and in the zero section X × {0} it is isomorphic to × X,1≤j≤ℓ

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“…The sheaf ρ −1 ν sa χ O w X is concentrated in degree zero. This follows from the following result of [4,5]…”

Section: We Denote By O Wmentioning

confidence: 78%

Multi-specialization and multi-asymptotic expansions

Honda¹,

Prelli²

2011

Proc. Japan Acad. Ser. A Math. Sci.

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show abstract

“…We refer to D'Agnolo‐Schapira 2, 3, and also to Kashiwara 15 for a specific study in the equivariant setting.…”

Section: Preliminariesmentioning

confidence: 99%

“…Proposition 3.4 (3, Lemma 3.1]) For \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\lambda ,\mu \in \big (\mathfrak {h}^*_{{}_{\mathbb {Z}}}\big )_{{}_{\mbox{{\sl I}}}}$\end{document} set then there is a natural isomorphism …”

Section: Integral Transforms On Dual Generalized Flag Manifoldsmentioning

confidence: 99%