By B. Moishezon

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**Extra info for Complex Surfaces and Connected Sums of Complex Projective Planes**

**Example text**

B ~ O. is diffeomorphic W e have ~ = Z to V ~ and Statement (2~+p+2g(S)-l)P (~) says that ~ (~+2p+2g(S)-l)Q. k Going b a c k to our a r g u m e n t s w i t h ~ : ~ of proof of the theorem) we see that ~ initial notations to ~ ~ (b-l)Q. >W (in the b e g i n n i n g is diffeomorphic Because in our ~ i is d i f f e o m o r p h i c to V 1 ~ P we get a d i f f e o m o r p h i s m vI / p ~ ~ # (2~+~+2g(s)-2)p # (~+2p+b+2g(s)-2)Q. Case 2). b = O. Let S 2 x S 2 = ~ , ~ = V 1 ~ $2 xx S 2 v I # s 2 x s2 ~ ~ be S 2 x S 2 and Statement by ~,~ means p ~ 2.

Of projective Because we need it in slightly modified give the main parts of its proof in the A p p e n d i x P. ~9). The result Theorem 3. singular any i = 1,2,---,q at a i is equal form, we shall to Part I (see is the following: Let V be an irreducible only isolated algebraic points, say the dimension to three. ,aq. jq : ~-l "I -l(ui) (Ui) (2) q TI(V) - ~ ( a i ) i=l (3) If N >_ 5, subspace singular in is biregular. has only ordinary V corresponding locus of Su(V) >U i V is not contained of ~pN and ~p2 in ~pS, curve Ui, ~(V) > ~pN singular points.

Is diffeomorphic W e have ~ = Z to V ~ and Statement (2~+p+2g(S)-l)P (~) says that ~ (~+2p+2g(S)-l)Q. k Going b a c k to our a r g u m e n t s w i t h ~ : ~ of proof of the theorem) we see that ~ initial notations to ~ ~ (b-l)Q. >W (in the b e g i n n i n g is diffeomorphic Because in our ~ i is d i f f e o m o r p h i c to V 1 ~ P we get a d i f f e o m o r p h i s m vI / p ~ ~ # (2~+~+2g(s)-2)p # (~+2p+b+2g(s)-2)Q. Case 2). b = O. Let S 2 x S 2 = ~ , ~ = V 1 ~ $2 xx S 2 v I # s 2 x s2 ~ ~ be S 2 x S 2 and Statement by ~,~ means p ~ 2.