Les singularités à l'infini des polynômes et les compactifications toriques
Alessandrini, David
Tohoku Math. J. (2), Tome 63 (2011) no. 1, p. 1-19 / Harvested from Project Euclid
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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.
Publié le : 2011-05-15
Classification:  Singularities at infinity,  toric varieties,  vanishing cycles,  non-caracteristic condition,  vector field,  32S30,  32S45,  32S60,  58K05,  58K55 
@article{1303219933,
     author = {Alessandrini, David},
     title = {Les singularit\'es \`a l'infini des polyn\^omes et les compactifications toriques},
     journal = {Tohoku Math. J. (2)},
     volume = {63},
     number = {1},
     year = {2011},
     pages = { 1-19},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1303219933}
}

Alessandrini, David. Les singularités à l'infini des polynômes et les compactifications toriques. Tohoku Math. J. (2), Tome 63 (2011) no. 1, pp.  1-19. http://gdmltest.u-ga.fr/item/1303219933/