By A. Campillo

ISBN-10: 3540100229

ISBN-13: 9783540100225

**Read Online or Download Algebroid Curves in Positive Characteristics PDF**

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**Extra info for Algebroid Curves in Positive Characteristics**

**Example text**

A0hx a l 2 z 12 + . . + a l h x = (D) {z I ,x } . . . 1zlhl+ . . . ° . . . , jI (ajl=O since , z. < U ( y ) . .. for which are expansion a curve, -- -- r ). - parametric @ k((u)), with the system t~erified provides parameter z by it. a : r X X(Z = r y = y(z r Sometimes, expansion by an we shal expression denote simply a H a m b u r g e r - N o e t h e r like h (D) together with coefficients with 0 Proposition { x,y } the a... JJ ~< r , z ~j For o 1) =x, z 2) z ji j + Z restrictions instance =y -1 The (D) (or Z .

XN}I curve primary prime, exceptional The by T(j). = -tP" i s (i . e . algebroid 1 ..... = {t I , . . , t s } 1 all of Tst(C) C, general) irredundant curves A(C) in of an transversal T(j). divisor C is r. 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)) , then It field. The which is is only complete. - algebroid for is ring algebraic of an parameter. such that the over k, irreducible Then [] (:::El (see is the × map r-~ : Spec(U ) Y ) T Y Y Y is bijective. Proof: Since is t r a n s v e r s a l x we have 0 C. ). x By the above lemma Spat([] ) consists of o n l y two ideals, (0) and x the maximal If y ~ ideal m- {0} mx. 5. - x a transversal of y -m- y equalities Definition is exactly two bijective, elements. Spec(E] ) y of local. has is = F maximal and t~, i s y t~ (m ) = t~ (m ) .

### Algebroid Curves in Positive Characteristics by A. Campillo

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