# On the intersection product of analytic cycles

Annales Polonici Mathematici (2000)

- Volume: 73, Issue: 2, page 135-146
- ISSN: 0066-2216

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topRams, Sławomir. "On the intersection product of analytic cycles." Annales Polonici Mathematici 73.2 (2000): 135-146. <http://eudml.org/doc/262587>.

@article{Rams2000,

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).},

author = {Rams, Sławomir},

journal = {Annales Polonici Mathematici},

keywords = {improper intersection; regular separation; extended index of intersection; index of intersection; intersection product; analytic cycles},

language = {eng},

number = {2},

pages = {135-146},

title = {On the intersection product of analytic cycles},

url = {http://eudml.org/doc/262587},

volume = {73},

year = {2000},

}

TY - JOUR

AU - Rams, Sławomir

TI - On the intersection product of analytic cycles

JO - Annales Polonici Mathematici

PY - 2000

VL - 73

IS - 2

SP - 135

EP - 146

AB - 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).

LA - eng

KW - improper intersection; regular separation; extended index of intersection; index of intersection; intersection product; analytic cycles

UR - http://eudml.org/doc/262587

ER -

## References

top- [AM] R. Achilles and M. Manaresi, Multiplicities of a bigraded ring and intersection theory, Math. Ann. 309 (1997), 573-591. Zbl0894.14005
- [ATW] R. Achilles, P. Tworzewski and T. Winiarski, On improper isolated intersection in complex analytic geometry, Ann. Polon. Math. 51 (1990), 21-36. Zbl0796.32006
- [BH] A. Borel et A. Haefliger, La classe d'homologie fondamentale d'un espace analytique, Bull. Soc. Math. France 89 (1961), 461-513. Zbl0102.38502
- [Cg] E. Cygan, Intersection theory and separation exponent in complex analytic geometry, Ann. Polon. Math. 69 (1998), 287-299. Zbl0924.32005
- [CKT] E. Cygan, T. Krasiński and P. Tworzewski, Separation at infinity and Łojasiewicz exponent of polynomial mappings, Invent. Math. 136 (1999), 75-87. Zbl0942.32003
- [CT] E. Cygan and P. Tworzewski, Proper intersection multiplicity and regular separation of analytic sets, Ann. Polon. Math. 59 (1994), 293-298. Zbl0847.32008
- [Dr] R. N. Draper, Intersection theory in analytic geometry, Math. Ann. 180 (1969), 175-204. Zbl0157.40502
- [R₁] S. Rams, Convergence of holomorphic chains, Ann. Polon. Math. 65 (1997), 227-234. Zbl0873.32005
- [R₂] S. Rams, Bézout-type theorems for certain analytic sets, Bull. Polish Acad. Sci. Math. 46 (1998), 277-283. Zbl0947.32002
- [T₁] P. Tworzewski, Isolated intersection multiplicity and regular separation of analytic sets, Ann. Polon. Math. 58 (1993), 213-219. Zbl0784.32005
- [T₂] P. Tworzewski, Intersection theory in complex analytic geometry, Ann. Polon. Math. 62 (1995), 177-191. Zbl0911.32018
- [TW₁] P. Tworzewski and T. Winiarski, Continuity of intersection of analytic sets, Ann. Polon. Math. 42 (1983), 387-393. Zbl0576.32013
- [TW₂] P. Tworzewski and T. Winiarski, Cycles of zeros of holomorphic mappings, Bull. Polish Acad. Sci. Math. 37 (1989), 95-101. Zbl0759.32015

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