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The tree model of a meromorphic plane curve
No full textWe associate with a plane meromorphic curve f a tree model T(f) based on its contact structure. Then we give a description of the y-derivative of f (resp. the Jacobian J(f, g)) in terms of T(f) (resp. T(f, g)). We also characterize the regularity of f in terms of its tree. © 2013 Springer-Verlag Italia.Abhyankar S. S., 1977, P INT S ALG GEOM KYO, P240; Abhyankar SS, 1999, P INDIAN AS-MATH SCI, V109, P117, DOI 10.1007-BF02841532; Assi A., 1999, MATH Z, V230, P16; Assi A, 1999, CR ACAD SCI I-MATH, V329, P625, DOI 10.1016-S0764-4442(00)80013-0; Barroso ERG, 2000, P LOND MATH SOC, V81, P1, DOI 10.1112-S0024611500012430; DELAMATA FD, 1994, COMPOS MATH, V92, P327; DELAMATA FD, 1994, LOND MATH S, V201, P61; KUO TC, 1977, TOPOLOGY, V16, P299, DOI 10.1016-0040-9383(77)90037-4; Maugendre H, 1998, ANN FS TOULOUSE, V7, P497; Maugendre H., J LONDON MATH SOC, V59, P207; Merle M., 1977, INVENT MATH, V41, P299; Wall C.T.C., 2004, LMS STUDENT TEXTS, V63; Zariski O., 1973, LECT CTR MATH ECOLE0
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