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Example text

The top h o r i z o n t a l map is an isomorphism, while the bottom is surjective by Remark follows. 4. 3 hold (cf. 1 and the assertion of [19]). This may be proved as before by pas- A ~ (pm)r to a linear space A d i f f e r e n t proof of Theorem Lm _ c pr(m+l)-i NOTES. 1(A) was given by Barth [19]. ing a b i r a t i o n a l c o r r e s p o n d e n c e between It depends upon construct- pm x ~m and p2m which reduces the a s s e r t i o n for the diagonal to the c o r r e s p o n d i n g statement for a linear space originally Lm c ~ 2 m (B) is due to Deligne [i0, ii], who proved it using the b i r a t i o n a l correspondence.

In the lies on a linear space (A) follows J o u a n o l o u [19]. x' £ f-l(u) ~ l ( f - l ( L /! ) , x ') + ~l(X,x') ,~l(X,x') The proof of c o n s i d e r a b l y the argument theorem, we may choose a point Ogus, Speiser, and r e c e n t l y by F a l t i n g s includ- [14]. I(B), Deligne [Ii] shows that there are in fact a r b i t r a r i l y small n e i g h b o r h o o d s of L such that (3). f-l(u) is connected. Goresky and M a c P h e r s o n D e l i g n e ' s w h i c h extends [23] have proved a c o n j e c t u r e of (B) to higher h o m o t o p y groups.

Two natural of 2n f × f of connected singularities being of the analogous applications projective intersection the apply. L. result 30 bounds the d i m e n s i o n tangent early sent to X normal Using if In of the of one wants branched to C to the a s s e r t i o n Zariski's which every is p r o v e d of the a r g u m e n t case, ~I(P 2 -C) Deligne's topy groups extension compact generalization Goresky and M a c P h e r s o n . Finally, For the One tion. theorems - list are (tamely on the ramified) An argument image using yields in §9.

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