Simple sheaves along dihedral Lagrangians |
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Authors: | Giuseppe Zampieri |
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Institution: | (1) Dipartimento di Matematica, v. Belzoni 7, 35131 Padova, Italy;(2) Department of Mathematics, University of Maryland, 20742 College Park, MD, USA |
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Abstract: | We prove the unicity of a complex of sheavesF whose microsupport is carried by a “dihedral” Lagrangian Λ ofT
* X (X=a real manifold) and which is simple with a prescribed shift at a regular point of Λ. Our method consists in reducing Λ,
by a real contact transformation, to the conormal bundle to aC
1-hypersuface, and then in using K-S 1, Prop. 6.2.1] in the variant of D'A-Z 1]. This is similar to Z 2] but more general,
since complex contact transformations and calculations of shifts are not required. We then consider the case of a complex
manifoldX, and obtain some vanishing theorems for the complex of “microfunctions along Λ” similar to those of A-G], A-H], K-S 1]
(cf. also D'A-Z 3 5], Z 2]). |
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Keywords: | |
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