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By A. Campillo

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A 02 X I h + X xh Z I Z Oh ' 1 ~ U(z 1) < O_(x). series in 2 in the case (A) h )-- X .... a 0 1 , (a0i the -- + ~ ~ X a02 becomes a~) i ) x i ( ~-~ = In a0q on, different ~ a Oq ~ the case , then because (B), again if the to be Now, and suppose L( {x',y'} L(D) = N they must and ) -- ~q turns a i >h a contradict have .... equality i=] which + { x,y} the Let be a system assertion us D' be with the consider another is such true an for that every expansion term system (D) expansion.

Let and k let be [] an be x the unique maximal ideal not in the the over k field given of charac- by +l 2 tp +p+ tp +p+l basis transversal of curve closed {x,y} of m_ element in the quadratic is transversal basis transform and {x,y/x of [] } is y/x not be of separable the , and it is separable. aim since that the Remark k((t))/ identity 2. - is If k thus k((t))/ 3 + t 3 + t Moreover, + a6t not has 6 + aGt normal. and 7 normal. + . • • Indeed, this characteristic of 3, for is trivial k((t)). the curve 4 x' is not normal.

X. -E--. . . D + (X) I 2) glueing 17-I(o) actually a divisor) Proj(k[~ 1 ..... ~N]) togeti~er is a c l o s e d isomorphic ' I in the obvious k-subscheme to the , ~ . +t M 2 , inclusion XN] X- I the type, ( 19 ) ) : Spec( A[ and ). of f i n i t e O. We n e e d (Bennet, (or a graded projective and the manner. fl (M) ,, BIM(A) II5 II ~ n ProJ(nO__oMJMn+l) is induced by the natural co ~ Proj( graded n e0 @ M n=o Thus, onto to such a point (al the ,... the closed directions O' ,aN). n+l n=o M points of J7-1(0) the origin represented scheme homomorphism > through may The ring ~ M n) n::o 7"1-1(O) correspond in by is .

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