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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Zampieri, G. Simple sheaves along dihedral Lagrangians. J. Anal. Math. 66, 331–344 (1995). https://doi.org/10.1007/BF02788828
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DOI: https://doi.org/10.1007/BF02788828