Microlocal study of topological Radon transforms and real projective duality

Advances in Mathematics

Volumn 212, Issue 1, 2007, Pages 191-224

  Matsui, Yutaka ^a   Takeuchi, Kiyoshi ^b  

^a UNIVERSITY OF TOKYO   (Japan)

^b UNIVERSITY OF TSUKUBA   (Japan)

Author keywords

Constructible functions; Dual varieties; Radon transforms

Indexed keywords

EID: 34047262707     PISSN: 00018708     EISSN: 10902082     Source Type: Journal    
DOI: 10.1016/j.aim.2006.10.001     Document Type: Article

References (34)

1. Arnold V.I. Singularities of Caustics and Wave Fronts. Math. Appl. vol. 62 (1987), Kluwer
2. Arnold V.I., Gusein-Zade S.M., and Varchenko A.N. Singularities of Differential Maps I (1985), Birkhäuser
3. Boman J., and Quinto E.T. Support theorems for real-analytic Radon transforms. Duke Math. J. 55 4 (1987) 943-948
4. Brylinski J.L. Transformations canoniques, dualité projective, théorie de Lefschetz, transformations de Fourier et sommes trigonométriques. Géométrie et analyse microlocales. Astérisque 140-141 (1986) 3-134
5. Comte G. Equisingularité réelle: nombres de Lelong et images polaires. Ann. Sci. École Norm. Sup. 33 (2000) 757-788
6. D'Agnolo A., and Schapira P. Radon-Penrose transform for D-modules. J. Funct. Anal. 139 2 (1996) 349-382
7. Dimca A. Milnor numbers and multiplicities of dual varieties. Rev. Roumaine Math. Pures Appl. 31 (1986) 535-538
8. Ernström L. Topological Radon transforms and the local Euler obstruction. Duke Math. J. 76 (1994) 1-21
9. Fischer G., and Piontkowski J. Ruled Varieties (2001), Vieweg
10. Gelfand I.M., Kapranov M.M., and Zelevinski A.V. Discriminants, Resultants and Multidimensional Determinants (1994), Birkhäuser
11. Griffiths P., and Harris J. Algebraic geometry and local differential geometry. Ann. Sci. École Norm. Sup. (4) 12 (1979) 355-452
12. Guillemin V., and Stenberg S. Geometric Asymptotics. Math. Surveys vol. 14 (1977), Amer. Math. Soc., Providence
13. Helgason S. The Radon Transform. Progr. Math. vol. 5 (1980), Birkhäuser, Boston
14. Ishikawa G., and Morimoto T. Solution surfaces of Monge-Ampère equations. Differential Geom. Appl. 14 2 (2001) 113-124
15. Kashiwara M. Index theorem for maximally overdetermined systems of linear differential equations. Proc. Japan Acad. 49 (1973) 803-804
16. Kashiwara M. Systems of Microdifferential Equations. Progr. Math. vol. 34 (1983), Birkhäuser, Boston
17. Kashiwara M. Index theorem for constructible sheaves. Astérisque 130 (1985) 193-209
18. Kashiwara M., and Schapira P. Microlocal study of sheaves. Astérisque 128 (1985)
19. Kashiwara M., and Schapira P. Sheaves on Manifolds. Grundlehren Math. Wiss. vol. 292 (1990), Springer, Berlin-Heidelberg-New York
20. MacPherson R. Chern classes for singular varieties. Ann. of Math. 100 (1974) 423-432
21. Matsui Y. Radon transforms of constructible functions on Grassmann manifolds. Publ. Res. Inst. Math. Sci. 42 2 (2006) 551-580
22. Y. Matsui, K. Takeuchi, Generalized Plücker-Teissier-Kleiman formulas for varieties with arbitrary dual defect, in: Proceedings of Australian-Japanese Workshop on Real and Complex Singularities, World Scientific, in press
23. Y. Matsui, K. Takeuchi, Topological Radon transforms and degree formulas for dual varieties, submitted for publication
24. Y. Matsui, K. Takeuchi, Projective duality and topological X-ray Radon transforms, in preparation
25. Parusinski A. Multiplicity of the dual variety. Bull. London Math. Soc. 23 (1991) 429-436
26. Schapira P. Operations on constructible functions. J. Pure Appl. Algebra 72 (1991) 83-93
27. Schapira P. Tomography of constructible functions. Lecture Notes in Comput. Sci. vol. 948 (1995), Springer, Berlin 427-435
28. Schürmann J. A general intersection formula for Lagrangian cycles. Compos. Math. 140 (2004) 1037-1052
29. Takeuchi K. Microlocal boundary value problem in higher codimensions. Bull. Soc. Math. France 124 (1996) 243-276
30. Tevelev E. Projective Duality and Homogeneous Spaces. Encyclopaedia Math. Sci. vol. 133 (2005), Springer
31. Trotman D. Une version microlocale de la condition (w) de Verdier. Ann. Inst. Fourier Grenoble 39 (1989) 825-829
32. Urabe T. Duality of the second fundamental form. Real Analytic and Algebraic Singularities. Nagoya/Sapporo/Hachioji, 1996. Pitman Res. Notes Math. Ser. vol. 381 (1998), Longman, Harlow 145-148
33. Viro O.Y. Some integral calculus based on Euler characteristics. Lecture Notes in Math. vol. 1346 (1988), Springer, Berlin 127-138
34. Wall C.T.C. Singular Points of Plane Curves. London Math. Soc. Student Texts vol. 63 (2004), Cambridge Univ. Press