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On the geometry of polynomial mappings at infinity. (Sur la géométrie à l’infini des applications polynomiales.) (English. French summary) Zbl 1396.14050
Summary: We associate to a given polynomial map from $$\mathbb{C}^2$$ to itself with nonvanishing Jacobian a variety whose homology or intersection homology describes the geometry of singularities at infinity of this map.

##### MSC:
 14P10 Semialgebraic sets and related spaces 14R15 Jacobian problem 32S20 Global theory of complex singularities; cohomological properties
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##### References:
 [1] Bochnak, J.; M., Coste; Roy, M.-F., Géométrie algébrique réelle, (1987), Springer · Zbl 0633.14016 [2] Goresky, M.; MacPherson, R., Intersection homology theory, Topology, 19, 2, 135-162, (1980) · Zbl 0448.55004 [3] Goresky, M.; MacPherson, R., Intersection homology. II, Invent. Math., 72, 77-129, (1983) · Zbl 0529.55007 [4] Hardt, R., Semi-algebraic local-triviality in semi-algebraic mappings, Amer. J. Math., 102, 2, 291-302, (1980) · Zbl 0465.14012 [5] Jelonek, Z., The set of point at which polynomial map is not proper, Ann. Polon. Math., 58, 3, 259-266, (1993) · Zbl 0806.14009 [6] Jelonek, Z., Testing sets for properness of polynomial mappings, Math. Ann., 315, 1, 1-35, (1999) · Zbl 0946.14039 [7] Jelonek, Z., Geometry of real polynomial mappings, Math. Z., 239, 2, 321-333, (2002) · Zbl 0997.14017 [8] Keller, O. H., Ganze cremonatransformationen monatschr, Math. Phys., 47, 229-306, (1939) · Zbl 0021.15303 [9] Kirwan, F.; Woolf, J., An Introduction to Intersection Homology Theory, (2006), Chapman & Hall/CRC · Zbl 1106.55001 [10] Mostowski, T., Some properties of the ring of Nash functions, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 3, 2, 245-266, (1976) · Zbl 0335.14001 [11] Valette, G.$$, L^∞$$ homology is an intersection homology, Adv. in Math., 231, 3-4, 1818-1842, (2012) · Zbl 1258.14024
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