Tohoku Mathematical Journal

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

David Alessandrini

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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

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

First available in Project Euclid: 19 April 2011

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Zentralblatt MATH identifier

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

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


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.

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