Download e-book for kindle: Algebroid Curves in Positive Characteristics by A. Campillo

By A. Campillo

ISBN-10: 3540100229

ISBN-13: 9783540100225

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Z J, j expansion _v ( z j . ) , larization 0 j-1 Hamburger-Noether and = iii) ii) h, hr The is n is J = oo repeated integers h a consequence simultaneously by J and from indution in that n i) on sequence depend J and the exactly only ii). minimum on We s h a l l number h. times, J F-I. prove of i) ) 59 quadratic transformations For M(E]) which = 0, the are needed curve is to desingularize regular and its M([--~) >0 El. expansion of type 2 y = ao] The result is that + . . evident. Let assume x + a02 x [] the tion h~pothesis for [] be a curve result to such holds [] 1 that for M- M(I--~') and using [] and < M.

O'(j) we such q (:: k [ [ X 1. 2. of curves a point transform will in where algebroid [-~""1 L e t the they ideas an = 1 (see assume transforms transform is transform quadratic (reducible components transformation the certain irreducible to total I I 1,3. I . , but embedded XN))/q) irreducible determines the E I , . . , X'N) }) g i v e n ' The of } E] 1 . e. ~ it is a " r e d u c i b l e I considered in t h i s w o r k ~ b y r e a s o n s q = 1. quadratic In union the q = P l N " " " f~-Pm transversal J by and curve.

T above, for transform. e. i large (If way, C is and , a normal enough, plane, for i large crossing of chapter for the we case shall N=2 introduce which will satellite be o f t e n and used in the . Let an ordinary of lying curves). To sequel an q irreducible made O. )). i defined the O infinitely be near the closed point 0 point of 0 of in a 2-space its i-th (=plane). order Take neighbourhood. e, is E(O 1 ) the transform is the connected of component E(O1), for i>~2. I It is evident Definition free that 1 respect O.

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Algebroid Curves in Positive Characteristics by A. Campillo

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