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ArticleOriginal scientific text

Title

Intersection theory and separation exponent in complex analytic geometry

Authors 1

Affiliations

  1. Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Abstract

We consider the intersection multiplicity of analytic sets in the general situation. We prove that it is a regular separation exponent for complex analytic sets and so it estimates the Łojasiewicz exponent. We also give some geometric properties of proper projections of analytic sets.

Keywords

ENG
multiplicity of proper and improper intersection, exponent of regular separation

Bibliography

  1. [ATW] R. Achilles, P. Tworzewski and T. Winiarski, On improper isolated intersection in complex analytic geometry, Ann. Polon. Math. 51 (1990), 21-36.
  2. [Ch] E. M. Chirka, Complex Analytic Sets, Kluwer Acad. Publ., 1989.
  3. [CKT] E. Cygan, T. Krasiński and P. Tworzewski, Separation at infinity and Łojasiewicz exponent of polynomial mappings, preprint IMUJ 1997/22, 1-9.
  4. [CT] E. Cygan and P. Tworzewski, Proper intersection multiplicity and regular separation of analytic sets, Ann. Polon. Math. 59 (1994), 293-298.
  5. [D] R. Draper, Intersection theory in analytic geometry, Math. Ann. 180 (1969), 175-204.
  6. [JKS] S. Ji, J. Kollár and B. Shiffman, A global Łojasiewicz inequality for algebraic varieties, Trans. Amer. Math. Soc. 329 (1992), 813-818.
  7. [K] J. Kollár, Sharp effective Nullstellensatz, J. Amer. Math. Soc. 1 (1988), 963-975.
  8. [Ł₁] S. Łojasiewicz, Ensembles semi-analytiques, I.H.E.S., Bures-sur-Yvette, 1965.
  9. [Ł₂] S. Łojasiewicz, Introduction to Complex Analytic Geometry, Birkhäuser, Basel, 1991.
  10. [Ł₃] S. Łojasiewicz, Sur la séparation régulière, Univ. Studi Bologna Sem. Geom. 1985, 119-121.
  11. [T₁] P. Tworzewski, Intersection of analytic sets with linear subspaces, Ann. Scuola Norm. Sup. Pisa (4) 17 (1990), 227-271.
  12. [T₂] P. Tworzewski, Intersection theory in complex analytic geometry, Ann. Polon. Math. 62 (1995), 177-191.
  13. [T₃] P. Tworzewski, Isolated intersection multiplicity and regular separation of analytic sets, Ann. Polon. Math. 58 (1993), 213-219.
  14. [TW₁] P. Tworzewski and T. Winiarski, Analytic sets with proper projections, J. Reine Angew. Math. 337 (1982), 68-76.
  15. [TW₂] P. Tworzewski and T. Winiarski, Cycles of zeroes of holomorphic mappings, Bull. Polish Acad. Sci. Math. 37 (1989), 95-101.
  16. [W] T. Winiarski, Continuity of total number of intersection, Ann. Polon. Math. 47 (1986), 155-178.
Annales Polonici Mathematici
1998/69/3
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Pages:
287-299
Main language of publication
English
Received
1997-11-17
Accepted
1998-04-07
Published
1998
Exact and natural sciences