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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.

Nous définissons la caractéristique d’Euler évanescente d’une surface torique normale X σ , nous donnons une formule pour la calculer, et nous associons ce nombre avec la seconde multiplicité polaire de X σ . Nous présentons aussi une formule pour l’obstruction d’Euler d’une fonction f:X σ et pour la différence entre l’obstruction d’Euler de l’espace X σ et l’obstruction d’Euler d’une fonction f. 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 X σ , we give a formula to compute it, and we relate this number with the second polar multiplicity of X σ . We also present a formula for the Euler obstruction of a function f:X σ and for the difference between the Euler obstruction of the space X σ and the Euler obstruction of a function f. As an application of this result we compute the Euler obstruction of a type of polynomial on a family of determinantal surfaces.

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DOI : https://doi.org/10.5802/afst.1439
@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, 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/}
}
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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