Bifurcation values of polynomial functions and perverse sheaves
Annales de l'Institut Fourier, Volume 70 (2020) no. 2, pp. 597-619.

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.

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.

Received: 2018-04-04
Accepted: 2019-03-12
Published online: 2020-05-28
DOI: https://doi.org/10.5802/aif.3320
Classification: 14F05,  14F43,  14M25,  32C38,  32S20
Keywords: bifurcation values, perverse sheaves, vanishing cycles
@article{AIF_2020__70_2_597_0,
     author = {Takeuchi, Kiyoshi},
     title = {Bifurcation values of polynomial functions and perverse sheaves},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {70},
     number = {2},
     year = {2020},
     pages = {597-619},
     doi = {10.5802/aif.3320},
     language = {en},
     url = {aif.centre-mersenne.org/item/AIF_2020__70_2_597_0/}
}
Takeuchi, Kiyoshi. Bifurcation values of polynomial functions and perverse sheaves. Annales de l'Institut Fourier, Volume 70 (2020) no. 2, pp. 597-619. doi : 10.5802/aif.3320. https://aif.centre-mersenne.org/item/AIF_2020__70_2_597_0/

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