Complex Surfaces and Connected Sums of Complex Projective by B. Moishezon

int(M2) > int(Ml) , ti: be simply-connected 2 t : D3XS 1 l . NT. = ~, T~ n T' = ~ for i ~ j, i,j = 1,2,3, T = ~ Ti, T' = ~ T i , l J l J i=l i=l a12,a13 6 ST1, al 2 ~ a13, a21 E 8T2, a31 E 8T3, aL2,a~3 E ~TI, t ~ ! w a~2 ~ a13 , a21 { ~T2, a31 E 8T~, ! y2,y3 (corresp. y2,Y}) be smooth disjoint paths in M 1 (corresp. M2) such that for j = 2,3 int yj c (int MI)-T (corresp.

7 0 : 71 : 72; z 3 ) ~ ) if z 3 = 0. some center its center with CZ) we obtain a map PK: ~K We can assume that the canonical of (where Ym" a manifold ~m: ~p1Xd m > d > ~plxd m is the G-process a non-singular complex m Tm' a map an open Wm: ~m is the canonical >dm projection with some center curve C m c ~ m such that 31 ~m - - : C Cm > d m unique branch is a ramified m point over Ym' a tubular of C m in Tm' an embedding Tm = ~m ~' m covering where T ~' : T m m of degree two with neighborhood > T--m with Pm: ~m ~ ' (Tm) = T m - ~m' = ~ n B' A Vl, and an annulus m m > Cm K m c d m with center Ym such that ~m ~ l ( K m ) ~ Using Lemma Vt t E A' = ~m " (Pro ~m-l(Km)D~m) 1 and the assumption we can identify can consider Denote m h-l(Vo ~ ) TC = h-l(Vo ~ ) that ~ with V;-VI~ as a regular is transveral %-h-l(Vo~ neighborhood and let the corresponding to ).

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