Abstract
Various topological properties of projective duality between real projective varieties and their duals are obtained by making use of the microlocal theory of (subanalytically) constructible sheaves developed by Kashiwara [M. Kashiwara, Index theorem for constructible sheaves, Astérisque 130 (1985) 193-209] and Kashiwara-Schapira [M. Kashiwara, P. Schapira, Sheaves on Manifolds, Grundlehren Math. Wiss., vol. 292, Springer, Berlin-Heidelberg-New York, 1990]. In particular, we prove in the real setting some results similar to the ones proved by Ernström in the complex case [L. Ernström, Topological Radon transforms and the local Euler obstruction, Duke Math. J. 76 (1994) 1-21]. For this purpose, we describe the characteristic cycles of topological Radon transforms of constructible functions in terms of curvatures of strata in real projective spaces.
Original language | English |
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Pages (from-to) | 191-224 |
Number of pages | 34 |
Journal | Advances in Mathematics |
Volume | 212 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2007 Jun 20 |
Externally published | Yes |
Keywords
- Constructible functions
- Dual varieties
- Radon transforms
ASJC Scopus subject areas
- Mathematics(all)