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2 - Dept. Math, Hokkaido Univ. EPrints Server

2 - Dept. Math, Hokkaido Univ. EPrints Server

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Coinbilling this with Toinari's result [19], we obtain the following :<br />

Corollary 3.4 Lei (If, P) be an isoluted singularity defined by<br />

r3 + h(z,y) = 0. Then we have p(P) 2 6pg(P).<br />

Problems 1) Show the analogous argument as in 53 for any 2-<br />

dilnensional hypersurface triple point.<br />

2) Construct the process of canonical resolution for surfaces of n-<br />

section type.<br />

The detail will be published in our forthcoming paper.<br />

References<br />

[I] S. Abhyanler: Local rings of high embedded dimension, Amer. J. Matll. 89<br />

(1967), 1073-1077.<br />

[2] 'I7. Ashiltaga and K. Konno: Examnples of degenerations of Castelnuovo surfaces,<br />

preprint .<br />

[3] A. Durfee: The signature of smoothings of complex surface singularities, <strong>Math</strong>.<br />

Ann. 232 (1978), 85-98.<br />

[4] A. Franchetta: Sui punti doppi isolati delle superficie algebriche, Note I and 11,<br />

Rend. Accad. dei Lincei (1946), 49-57, 162-165.<br />

[5] E. Horiltawa: On deformations of quintic surfaces, Invent. <strong>Math</strong>. 31 (1975), 43-85.<br />

[6] E. I-Torikawa: Algebraic surfaces of general type with small c:, I, 11, 111, IV,<br />

'V, Ann. <strong>Math</strong>. 104 (1976), 358-387, Invent. <strong>Math</strong>. 37 (1976), 121-155, ibid. 47<br />

(197S), 209-248, ibid. 50 (1979), 103-128, J. Fac. Sci. <strong>Univ</strong>. Tolryo 28 (1981),<br />

745-755.<br />

[7] D. Kirby: The structure of an isolated multiple point of a surface I, 11, 111, Proc.<br />

London <strong>Math</strong>. Soc. (3) V1 (1956), 597-609, VII (1957), 1-25.<br />

[S] 13. Laufer: On minimally elliptic singularities, Amer. J. <strong>Math</strong>. 99 (1977), 1257-<br />

1295.<br />

[9] 13. Laufer: On p For surface singularities, in PTOC.<br />

of Symposia in Pure &lath. 30<br />

(1977), 45-49.

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