Une propriété asymptotique des puissances symboliques d'un idéal. Application à la théorie de l'intersection sur les surfaces normales

Marcelo Morales

Annales de l'institut Fourier (1982)

  • Volume: 32, Issue: 2, page 219-228
  • ISSN: 0373-0956

Abstract

top
We express the intersection multiplicity of two curves which intersect at a singular point of a normal surface in terms of valuations. It generalizes the known result for a regular surface. We use the definitions given by Mumford and we study also the total transform of a curve by a resolution of singularities.

How to cite

top

Morales, Marcelo. "Une propriété asymptotique des puissances symboliques d'un idéal. Application à la théorie de l'intersection sur les surfaces normales." Annales de l'institut Fourier 32.2 (1982): 219-228. <http://eudml.org/doc/74537>.

@article{Morales1982,
abstract = {Nous exprimons la multiplicité d’intersection de deux courbes se coupant au point singulier d’une surface normale en termes de valuations. C’est une généralisation du résultat connu pour les surfaces régulières.},
author = {Morales, Marcelo},
journal = {Annales de l'institut Fourier},
keywords = {multiplicity; intersection of curves; surface singularity; resolution},
language = {fre},
number = {2},
pages = {219-228},
publisher = {Association des Annales de l'Institut Fourier},
title = {Une propriété asymptotique des puissances symboliques d'un idéal. Application à la théorie de l'intersection sur les surfaces normales},
url = {http://eudml.org/doc/74537},
volume = {32},
year = {1982},
}

TY - JOUR
AU - Morales, Marcelo
TI - Une propriété asymptotique des puissances symboliques d'un idéal. Application à la théorie de l'intersection sur les surfaces normales
JO - Annales de l'institut Fourier
PY - 1982
PB - Association des Annales de l'Institut Fourier
VL - 32
IS - 2
SP - 219
EP - 228
AB - Nous exprimons la multiplicité d’intersection de deux courbes se coupant au point singulier d’une surface normale en termes de valuations. C’est une généralisation du résultat connu pour les surfaces régulières.
LA - fre
KW - multiplicity; intersection of curves; surface singularity; resolution
UR - http://eudml.org/doc/74537
ER -

References

top
  1. [1] M. ARTIN, On isolated rational singularities of surfaces, Amer. J. of Maths., 88, (1966), 129-136. Zbl0142.18602MR33 #7340
  2. [2] J. GIRAUD, Improvement of Grauert-Riemenschneider's theorem for a normal surface, à paraître. Zbl0488.32013
  3. [3] A. GROTHENDIECK, E.G.A. III, Pub. Math. IHES, n° 11 (1961). 
  4. [4] R. HARTSHORNE, Algebraic geometry, 1977, Springer-Verlag. Zbl0367.14001MR57 #3116
  5. [5] J. LIPMAN, Rational singularities... Pub. Math. IHES, n° 36 (1969). Zbl0181.48903
  6. [6] D. MUMFORD, The topology of normal singularities of an algebraic surface and a criterion for simplicity, Pub. Math. IHES, n° 9 (1961). Zbl0108.16801MR27 #3643
  7. [7] C. P. RAMANUJAM, Remarks on the Kodaira Vanishing Theorem, Journal of the Indian Math. Soc., 36 (1972), 41-51. Zbl0276.32018MR48 #8502
  8. [8] REEVE, A note on fractional intersection multiplicities, Rend. Circolo Mat. Palermo, 1 (1958). Zbl0086.14302MR23 #A2109
  9. [9] P. SAMUEL, Multiplicités de certaines composantes singulières, III. J. Math., 3 (1959). Zbl0096.35801MR21 #4159
  10. [10] ZARISKI-SAMUEL, Algèbre commutative. (Vol. I, II), Van Nostrand, Princeton (1958, 1960). 

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.