Tohoku Mathematical Journal

Les singularités à l'infini des polynômes et les compactifications toriques

David Alessandrini

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Abstract

We study the toric compactifications of fibers of a polynomial mapping in several complex variables and analyse their singularities which can appear at infinity. We compare severals possible definitions of such singularities. Essentially, these definitions are related to the topological triviality, the non-characteristic condition, the gradient condition and the absence of vanishing cycles at infinity. We generalize to the toric compactification set-up the results known for the projective compactification.

Article information

Source
Tohoku Math. J. (2), Volume 63, Number 1 (2011), 1-19.

Dates
First available in Project Euclid: 19 April 2011

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1303219933

Digital Object Identifier
doi:10.2748/tmj/1303219933

Mathematical Reviews number (MathSciNet)
MR2788773

Zentralblatt MATH identifier
1226.32015

Subjects
Primary: 32S30: Deformations of singularities; vanishing cycles [See also 14B07]
Secondary: 32S45: Modifications; resolution of singularities [See also 14E15] 32S60: Stratifications; constructible sheaves; intersection cohomology [See also 58Kxx] 58K05: Critical points of functions and mappings 58K55: Asymptotic behavior

Keywords
Singularities at infinity toric varieties vanishing cycles non-caracteristic condition vector field

Citation

Alessandrini, David. Les singularités à l'infini des polynômes et les compactifications toriques. Tohoku Math. J. (2) 63 (2011), no. 1, 1--19. doi:10.2748/tmj/1303219933. https://projecteuclid.org/euclid.tmj/1303219933


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