HOME > Table of Contents and Abstracts > Vol. 63, No. 1
Tohoku Mathematical Journal
SECOND SERIES VOL. 63, NO. 1
|Tohoku Math. J.|
63 (2011), 1-19
LES SINGULARITÉS À L'INFINI DES POLYNÔMES ET LES COMPACTIFICATIONS TORIQUES
(Received December 3, 2009, revised July 20, 2010)
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.
2000 Mathematics Subject Classification.
Primary 32S30; Secondary 32S45, 32S60, 58K05, 58K55.
Key words and phrases.
Singularities at infinity, toric varieties, vanishing cycles, non-caracteristic condition, vector field.
To the top of this page
Back to the Contents