By Igor Dolgachev, Anatoly Libgober (auth.), Anatoly Libgober, Philip Wagreich (eds.)

ISBN-10: 3540108335

ISBN-13: 9783540108337

ISBN-10: 354038720X

ISBN-13: 9783540387206

**Read or Download Algebraic Geometry: Proceedings of the Midwest Algebraic Geometry Conference, University of Illinois at Chicago Circle, May 2 – 3, 1980 PDF**

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**Additional info for Algebraic Geometry: Proceedings of the Midwest Algebraic Geometry Conference, University of Illinois at Chicago Circle, May 2 – 3, 1980**

**Sample text**

Of d i m e n s i o n n , and let f : X ÷ ~n be a finite morphism. e. 1. ef(x) The proof theorem of p r o j e c t i v e ([20]) (A) >- m i n ( d , will generalizes yield There space exists ramification U c X £+I image in is the pn a stronger loci set of , then £ < min(d Proof n = 1 If L c pn * the n ~ 2 , the In t h e fact that every ramify. at l e a s t one point x e X at are i ef(x) closed Namely, R£ = U n A x the sets > £} algebraic (£+l)-tuples consider subsets of d i s t i n c t We will of points show that X : for if with the same in f a c t , X) ~ £ - i, n) of T h e o r e m being must statement.

X* + ÷ ~I(X) in and the is , X* a complex provided topology. The previous arguments. from given map over X to p a s s being in t h e surjective classical simplifies construction p2m+l Moreover the { -bundle proof In f to The m assertions where on f-l(A) L c p2m+l is here t h e B e r t i n i In to the cerns §§4 - 7 we by c o n s i d e r i n g that the X n Y is that The proof map F = are if allows pair one to to the of a theorem to the of at least degree n + 1 or more a generalization sheeted Zak on that of of this In to f*-l(L) , and if smooth the give will and varieties.

That is a f i n i t e C curve C c X be the image (by C o r o l l a r y imply that 5~3), the homo- C must morphism ker(HiC is s u r j e c t i v e . have large Thus from r~nified, many when geometric which purposes say t h a t ramified of X is large, X Xy X flexible is w e a k l y degenerated pair (p*,q*) through with from image exists in pairs Y Loosely speaking, be r a m i f i e d . As (p,q) will However double any can points an i m m e d i a t e AX is a conf is f : X + Y points be c o n t i n u of generically be w e a k l y for Let us of d i s t i n c t (p,q) example, to a s u r f a c e if structures; that is is s u f f i c i e n t .

### Algebraic Geometry: Proceedings of the Midwest Algebraic Geometry Conference, University of Illinois at Chicago Circle, May 2 – 3, 1980 by Igor Dolgachev, Anatoly Libgober (auth.), Anatoly Libgober, Philip Wagreich (eds.)

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