Real analytic desingularization and subanalytic sets: an elementary approach
HTML articles powered by AMS MathViewer
- by H. J. Sussmann PDF
- Trans. Amer. Math. Soc. 317 (1990), 417-461 Request permission
Abstract:We give a proof of a theorem on desingularization of real-analytic functions which is a weaker version of H. Hironaka’s result, but has the advantage of being completely self-contained and elementary, and not involving any machinery from algebraic geometry. We show that the basic facts about subanalytic sets can be proved from this result.
- Edward Bierstone and Pierre D. Milman, Semianalytic and subanalytic sets, Inst. Hautes Études Sci. Publ. Math. 67 (1988), 5–42. MR 972342, DOI 10.1007/BF02699126
- A. M. Gabrièlov, Projections of semianalytic sets, Funkcional. Anal. i Priložen. 2 (1968), no. 4, 18–30 (Russian). MR 0245831
- Robert M. Hardt, Stratification of real analytic mappings and images, Invent. Math. 28 (1975), 193–208. MR 372237, DOI 10.1007/BF01436073
- Robert M. Hardt, Topological properties of subanalytic sets, Trans. Amer. Math. Soc. 211 (1975), 57–70. MR 379882, DOI 10.1090/S0002-9947-1975-0379882-8
- Robert M. Hardt, Triangulation of subanalytic sets and proper light subanalytic maps, Invent. Math. 38 (1976/77), no. 3, 207–217. MR 454051, DOI 10.1007/BF01403128
- Robert M. Hardt, Stratification via corank one projections, Singularities, Part 1 (Arcata, Calif., 1981) Proc. Sympos. Pure Math., vol. 40, Amer. Math. Soc., Providence, RI, 1983, pp. 559–566. MR 713092
- Heisuke Hironaka, Subanalytic sets, Number theory, algebraic geometry and commutative algebra, in honor of Yasuo Akizuki, Kinokuniya, Tokyo, 1973, pp. 453–493. MR 0377101
- Heisuke Hironaka, Triangulations of algebraic sets, Algebraic geometry (Proc. Sympos. Pure Math., Vol. 29, Humboldt State Univ., Arcata, Calif., 1974) Amer. Math. Soc., Providence, R.I., 1975, pp. 165–185. MR 0374131
- B. O. Koopman and A. B. Brown, On the covering of analytic loci by complexes, Trans. Amer. Math. Soc. 34 (1932), no. 2, 231–251. MR 1501636, DOI 10.1090/S0002-9947-1932-1501636-9 S. Lojasiewicz, Ensembles semianalytiques, Notes, Inst. Hautes Études, Bures-sur-Yvette, 1965.
- S. Lojasiewicz, Triangulation of semi-analytic sets, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 18 (1964), 449–474. MR 173265 H. J. Sussman, Subanalytic sets, stratifications and desingularization, Rutgers Univ. Press (to appear).
- © Copyright 1990 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 317 (1990), 417-461
- MSC: Primary 32B20; Secondary 32C45
- DOI: https://doi.org/10.1090/S0002-9947-1990-0943608-5
- MathSciNet review: 943608