360 M Furushima

We put <f,=[«,,,, . ,и, i]and5, = [n,,,, . ,И(2] Smcen, ^^^2, vie have ^,^r, + l, ^t>4i>^ By (1 6), we have easily

( 1 . 7 ) /.(Я.1 + 1)-^.(Яо + 1)=1 iluiui)

( 1 . 8 ) (Ао + 1)ио + ДЛ,1 + 1) = 1

( 1 . 9 ) (^ + 1)("о+Д|^) + д} = 1

Since (/i, ^2, ^з)=(3,3,3), (2,4,4), (2,3,6), (2,3,5), (2,3,4), (2,3,3), we have (1) iy = io(^u(г.(ъ)=(3,3,3),(2,4,4),(2,3,6)

1=1^1

( и ) i } > 1 <* (^1. «^2. h)=(2,3,5), (2,3,4), (2,3,3)

Case (I) i} = l

In this case, by (19), we have (Яо + 1)( "0+ E %) =0 By (17),

we have Я(,+1 фО Hence, £ ^ +Ио=0 Since «oè —2, we must have По= —1

or -2. If „„ = -1, then ;: have {%%^\4\}Л {\X}\ {'-}Л ° \ЛV2V3; \3'3'3/ \2'4'4/ \2'3'6/

Thus we have the dual graphs F. 4, F 5, and F 6, respectively If Ио= -2, then

graphs F 7, F 8, and F 9, respectively

CaseOO Iy>l. 1=1^^1

In this case, we have

- ( Ao + l)= ij-ijiy+noeZ

Hence , we have Ио= -1 or -2 If По= -1, then we have (|^,|^,|^) = (x,:^,:r),

/ 1 1 A /1 1 W ^^' ^' ^^^ ^^ ^ ^^

17'i'Ir 15'q'^) ^^^ ^o~ ~"2- '^'^^^^ ^^ ^^^^^ ^be dual graphs F 10, F. И, and

F 12, respectively If «о = - X then - (A^ -f 1) = I 7- -1 / I 7^ - 2 is not integer

1=1^1 / ï=it|

Hence «0+^2. Thus, we have finally the dual graphs F. 4-F. 12

( 4 ) The case where С is of the type (e)

Since max{nj ^0, repeating blowing ups and elementary transformations on

С as before, we have the'dual graphs F 13, F 14 and the following Fig. 19

( g \------f ю j ("^l)---------

Figa9

\