Nous définissons la caractéristique d’Euler évanescente d’une surface torique normale , nous donnons une formule pour la calculer, et nous associons ce nombre avec la seconde multiplicité polaire de . Nous présentons aussi une formule pour l’obstruction d’Euler d’une fonction et pour la différence entre l’obstruction d’Euler de l’espace et l’obstruction d’Euler d’une fonction . Comme application de ce résultat nous calculons l’obstruction d’Euler des polynômes d’un certain type sur une famille de surfaces déterminantales.
We define the vanishing Euler characteristic of a normal toric surface , we give a formula to compute it, and we relate this number with the second polar multiplicity of . We also present a formula for the Euler obstruction of a function and for the difference between the Euler obstruction of the space and the Euler obstruction of a function . As an application of this result we compute the Euler obstruction of a type of polynomial on a family of determinantal surfaces.
@article{AFST_2015_6_24_1_1_0,
author = {Tha{\'\i}s Maria Dalbelo and Nivaldo de G\'oes Grulha Jr. and Miriam Silva Pereira},
title = {Toric surfaces, vanishing {Euler} characteristic and {Euler} obstruction of a function},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {1--20},
publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 24},
number = {1},
year = {2015},
doi = {10.5802/afst.1439},
mrnumber = {3325948},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1439/}
}
TY - JOUR AU - Thaís Maria Dalbelo AU - Nivaldo de Góes Grulha Jr. AU - Miriam Silva Pereira TI - Toric surfaces, vanishing Euler characteristic and Euler obstruction of a function JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2015 SP - 1 EP - 20 VL - 24 IS - 1 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1439/ DO - 10.5802/afst.1439 LA - en ID - AFST_2015_6_24_1_1_0 ER -
%0 Journal Article %A Thaís Maria Dalbelo %A Nivaldo de Góes Grulha Jr. %A Miriam Silva Pereira %T Toric surfaces, vanishing Euler characteristic and Euler obstruction of a function %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2015 %P 1-20 %V 24 %N 1 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1439/ %R 10.5802/afst.1439 %G en %F AFST_2015_6_24_1_1_0
Thaís Maria Dalbelo; Nivaldo de Góes Grulha Jr.; Miriam Silva Pereira. Toric surfaces, vanishing Euler characteristic and Euler obstruction of a function. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 24 (2015) no. 1, pp. 1-20. doi : 10.5802/afst.1439. https://afst.centre-mersenne.org/articles/10.5802/afst.1439/
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