Microlocal study of topological Radon transforms and real projective duality

• Autores: Yutaka Matsui, Kiyoshi Takeuchi
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 212, Nº 1, 2007, págs. 191-224
• Idioma: inglés
• DOI: 10.1016/j.aim.2006.10.001
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• Resumen

  • 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.