Microlocal study of topological Radon transforms and real projective duality

Yutaka Matsui, Kiyoshi Takeuchi

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

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 languageEnglish
Pages (from-to)191-224
Number of pages34
JournalAdvances in Mathematics
Volume212
Issue number1
DOIs
Publication statusPublished - 2007 Jun 20
Externally publishedYes

Keywords

  • Constructible functions
  • Dual varieties
  • Radon transforms

ASJC Scopus subject areas

  • Mathematics(all)

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