Existence des diviseurs dicritiques, d’après S.S. Abhyankar
Vincent CossartUniversité de Versailles Saint-Quentin, Versailles, France
Mickaël MatusinskiUniversité Bordeaux 1, Talence, France
Guillermo Moreno-SocíasCNRS/UVSQ, Versailles, France
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In this article, there are new proofs of the existence and unicity of dicritical divisors of a pencil of plane curves of Incidentally, we prove the equivalence between dicritical divisors and Rees valuations. Furthermore, in the case where is regular at the base points of , we have that is residually a polynomial along any dicritical divisor; this reproves geometrically [2, Theorem (7.1)]. As a corollary of the latter proof, we get a generalization of the connectedness theorem of .