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B I B o notations: h k + l n k + l + . +"h nk~ hk_l If marked use boxes which d rows and 1 I ... is =n) (n o e-1 n e - 1 + n e ~ } hj_]nj_l+ nj I B ) is j-1 compatible for all k( a matrix with e, j} of then O there (B exists I B o 1 of I B I B. I . b) marked a matrix Let boxes nk / hk+l d+l rows (B +... and I + nj ... -1 o first can integers be e ~d ~ We It all J only can to is k< j. + nk> be the e exists with e a matrix of of type h whole B h j-] chosen whithout J account any that n j-I and at most + n.

1). ,. + q-1 i=0 a q - 1 be i its x = t , i x ( el, +i)/c~ 1 " q-1 "''aq-l+ Puiseux series~ or~ if [~] ~ (C~'q+i)/c~ . . i=0 a q , l . x 1 ~q we w i s h power series of a parameter t, n h h y = ~ i =1 a i t n i h 1 +'~i=Oal, 't(ct'lti)cl2"''ctq + ... q-1 + ~i=0 a q - 1 , t ( a ' q - l + i ) c ~ q ' ~o + ~q i=0 a q ' i t where n = c~1 . . ~ we = 1, a . ,q, We r e c a l l and determines chosen, its except a substitution that a. J the characteristic to some t e r m s describe is of the term how cLj_ 1 + h j _ 1 + 1 to v a n i s h .

Lecture interpretation multiplicit& Proceedings Notes the algebr d'une London que branche de la suite des algebrique". Mathematical Society (2),vol. 256-28?. "Algebroid in ) o Curves Mathematics, in Positive vol . Spr Characteristic" nger-Verlag. "La curva alabeada". Central 1:43 P. proyecciGn Du de [6] de on branche alg~brique". Soci (2), vol . J. Lipman. of Mathematics, Cahit la s u i t e vol. Geometrfa. "AI New (1972). "Teori Bologna, O. 288-294. Jansichelli, [7] -° d e de Barcelona. Dpt Val .