no. 5
On the geometry of polynomial mappings at infinity
[Sur la géométrie à l’infini des applications polynomiales]
Valette, Anna1 ; Valette, Guillaume2
1 Instytut Matematyki Uniwersytetu Jagiellońskiego, ul. S Łojasiewicza, Kraków, Poland
2 Instytut Matematyczny PAN, ul. Św. Tomasza 30, 31-027 Kraków, Poland
Annales de l'Institut Fourier, Tome 64 (2014) no. 5, pp. 2147-2163.

On associe à une application polynomiale de ℂ 2 dans lui-même à Jacobien constant non nul, une variété dont l’homologie ou l’homologie d’intersection décrit la géométrie à l’infini de cette application.

We associate to a given polynomial map from ℂ 2 to itself with nonvanishing Jacobian a variety whose homology or intersection homology describes the geometry of singularities at infinity of this map.

DOI : 10.5802/aif.2907
Classification : 14P10, 14R15, 32S20, 55N33
Keywords: complex polynomial mappings, singularities at infinity, asymptotical values, intersection homology, Jacobian conjecture.
Mot clés : singularités à l’infini, valeurs asymptotiques, homologie d’intersection, conjecture Jacobienne.

Valette, Anna 1 ; Valette, Guillaume 2

1 Instytut Matematyki Uniwersytetu Jagiellońskiego, ul. S Łojasiewicza, Kraków, Poland
2 Instytut Matematyczny PAN, ul. Św. Tomasza 30, 31-027 Kraków, Poland 
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Valette, Anna; Valette, Guillaume. On the geometry of polynomial mappings at infinity. Annales de l'Institut Fourier, Tome 64 (2014) no. 5, pp. 2147-2163. doi : 10.5802/aif.2907. https://aif.centre-mersenne.org/articles/10.5802/aif.2907/

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