no. 2
Bifurcation values of polynomial functions and perverse sheaves
[Les valeurs de bifurcation de fonctions polynomiales et faisceaux pervers]
Takeuchi, Kiyoshi1
1 Institute of Mathematics, University of Tsukuba 1-1-1, Tennodai, Tsukuba, Ibaraki, 305-8571 (Japan)
Annales de l'Institut Fourier, Tome 70 (2020) no. 2, pp. 597-619.

Nous caractérisons les valeurs de bifurcation de fonctions polynomiales en utilisant la théorie des faisceaux pervers et leurs cycles évanescents. En particulier, en introduisant une méthode pour calculer les sauts de caractéristiques d’Euler à support compact de leurs fibres, nous confirmons la conjecture de Némethi–Zaharia dans de nombreux cas.

We characterize bifurcation values of polynomial functions by using the theory of perverse sheaves and their vanishing cycles. In particular, by introducing a method to compute the jumps of the Euler characteristics with compact support of their fibers, we confirm the conjecture of Némethi–Zaharia in many cases.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/aif.3320
Classification : 14F05, 14F43, 14M25, 32C38, 32S20
Keywords: bifurcation values, perverse sheaves, vanishing cycles
Mot clés : valeurs de bifurcation, faisceaux pervers, cycles évanescents
Takeuchi, Kiyoshi 1

1 Institute of Mathematics, University of Tsukuba 1-1-1, Tennodai, Tsukuba, Ibaraki, 305-8571 (Japan)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Takeuchi, Kiyoshi. Bifurcation values of polynomial functions and perverse sheaves. Annales de l'Institut Fourier, Tome 70 (2020) no. 2, pp. 597-619. doi : 10.5802/aif.3320. https://aif.centre-mersenne.org/articles/10.5802/aif.3320/

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