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ArticleOriginal scientific text

Title

On the intersection product of analytic cycles

Authors 1

Affiliations

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

Abstract

We prove that the generalized index of intersection of an analytic set with a closed submanifold (Thm. 4.3) and the intersection product of analytic cycles (Thm. 5.4), which are defined in [T₂], are intrinsic. We define the intersection product of analytic cycles on a reduced analytic space (Def. 5.8) and prove a relation of its degree and the exponent of proper separation (Thm. 6.3).

Keywords

ENG
improper intersection, regular separation, extended index of intersection

Bibliography

  1. [AM] R. Achilles and M. Manaresi, Multiplicities of a bigraded ring and intersection theory, Math. Ann. 309 (1997), 573-591.
  2. [ATW] R. Achilles, P. Tworzewski and T. Winiarski, On improper isolated intersection in complex analytic geometry, Ann. Polon. Math. 51 (1990), 21-36.
  3. [BH] A. Borel et A. Haefliger, La classe d'homologie fondamentale d'un espace analytique, Bull. Soc. Math. France 89 (1961), 461-513.
  4. [Cg] E. Cygan, Intersection theory and separation exponent in complex analytic geometry, Ann. Polon. Math. 69 (1998), 287-299.
  5. [CKT] E. Cygan, T. Krasiński and P. Tworzewski, Separation at infinity and Łojasiewicz exponent of polynomial mappings, Invent. Math. 136 (1999), 75-87.
  6. [CT] E. Cygan and P. Tworzewski, Proper intersection multiplicity and regular separation of analytic sets, Ann. Polon. Math. 59 (1994), 293-298.
  7. [Dr] R. N. Draper, Intersection theory in analytic geometry, Math. Ann. 180 (1969), 175-204.
  8. [R₁] S. Rams, Convergence of holomorphic chains, Ann. Polon. Math. 65 (1997), 227-234.
  9. [R₂] S. Rams, Bézout-type theorems for certain analytic sets, Bull. Polish Acad. Sci. Math. 46 (1998), 277-283.
  10. [T₁] P. Tworzewski, Isolated intersection multiplicity and regular separation of analytic sets, Ann. Polon. Math. 58 (1993), 213-219.
  11. [T₂] P. Tworzewski, Intersection theory in complex analytic geometry, Ann. Polon. Math. 62 (1995), 177-191.
  12. [TW₁] P. Tworzewski and T. Winiarski, Continuity of intersection of analytic sets, Ann. Polon. Math. 42 (1983), 387-393.
  13. [TW₂] P. Tworzewski and T. Winiarski, Cycles of zeros of holomorphic mappings, Bull. Polish Acad. Sci. Math. 37 (1989), 95-101.
Annales Polonici Mathematici
2000/73/2
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Pages:
135-146
Main language of publication
English
Received
1999-05-06
Accepted
1999-09-27
Published
2000
Exact and natural sciences