On the intersection product of analytic cycles

Sławomir Rams

Annales Polonici Mathematici (2000)

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

Abstract

top
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).

How to cite

top

Rams, 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
  1. [AM] R. Achilles and M. Manaresi, Multiplicities of a bigraded ring and intersection theory, Math. Ann. 309 (1997), 573-591. Zbl0894.14005
  2. [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
  3. [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
  4. [Cg] E. Cygan, Intersection theory and separation exponent in complex analytic geometry, Ann. Polon. Math. 69 (1998), 287-299. Zbl0924.32005
  5. [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
  6. [CT] E. Cygan and P. Tworzewski, Proper intersection multiplicity and regular separation of analytic sets, Ann. Polon. Math. 59 (1994), 293-298. Zbl0847.32008
  7. [Dr] R. N. Draper, Intersection theory in analytic geometry, Math. Ann. 180 (1969), 175-204. Zbl0157.40502
  8. [R₁] S. Rams, Convergence of holomorphic chains, Ann. Polon. Math. 65 (1997), 227-234. Zbl0873.32005
  9. [R₂] S. Rams, Bézout-type theorems for certain analytic sets, Bull. Polish Acad. Sci. Math. 46 (1998), 277-283. Zbl0947.32002
  10. [T₁] P. Tworzewski, Isolated intersection multiplicity and regular separation of analytic sets, Ann. Polon. Math. 58 (1993), 213-219. Zbl0784.32005
  11. [T₂] P. Tworzewski, Intersection theory in complex analytic geometry, Ann. Polon. Math. 62 (1995), 177-191. Zbl0911.32018
  12. [TW₁] P. Tworzewski and T. Winiarski, Continuity of intersection of analytic sets, Ann. Polon. Math. 42 (1983), 387-393. Zbl0576.32013
  13. [TW₂] P. Tworzewski and T. Winiarski, Cycles of zeros of holomorphic mappings, Bull. Polish Acad. Sci. Math. 37 (1989), 95-101. Zbl0759.32015

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.