(1) There exists a P 1 -fibration h: Xâ )C over a curve C such that Supp (D) ..... G, which is a fiber of a minimal elliptic fibration on a nonsingular surface Xo,.
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J. Math. Kyoto U niv. (JMKYAZ) 38-1 (1998) 77-99
Almost minimal embeddings of quotient singular points into rational surfaces By Hideo
KOJIMA
O. Introduction Let k b e a n algebraically closed field of characteristic z e r o . L e t X b e a normal algebraic surface w ith only one quotient singular point P . Let f: X — )
X be a minimal resolution of X and let D = E7=1D, be th e reduced exceptional divisor w ith respect to f, w here the D i a re irreducible com ponents. D efine a Q divisor D u = Er= cr D s u c h t h a t (D# K x • Di ) = 0 f o r e v e ry 1 Since the intersection m atrix of D is negative definite a n d (Dy) — 2, I)* is uniquely defined and 0 2)