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

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

**Example text**

Be the n o r m a l i z a t i o n i n d u c e d map. ×i~m X r ) - - - ~ Z l ( X 1 × . . 1(B) surjective. surjective, and the applies to But the Corollary • (I) the C o r o l l a r y Hironaka when f and Matsumura is s u r j e c t i v e . [36] h a d p r o v e d The t h e o r e m assertion (A) of s t a t e d by B a r t h in 45 [4] was zation Rossi the special of a s u b v a r i e t y of the c o r o l l a r y of pm The conjecture in varieties, and then f-l(y) dimf(X) and the [19] if f : X ÷ Z if that Y Z-~ Z would be c o n n e c t e d is a m o r p h i s m with Hansen (cf.

Singularities §6. Branched §7. Zak's T h e o r e m §8. The F u n d a m e n t a l §9. Higher §i0. Open Conventions, Linear and P r e l i m i n a r y Facts Sections Linear Sections Theorem of M a p p i n g s Coverings to P r o j e c t i v e of P r o j e c t i v e on T a n g e n c i e s Space Space and H a r t s h o r n e ' s Group of the C o m p l e m e n t of a Node Homotopy Questions References * Partially supported by NSF Grant Conjecture MCS78-04008. Curve 27 INTRODUCTION A recent of q u e s t i o n s several in a l g e b r a i c surprising projective of [16].

19]) let f : X + and then f Recall p. ample proved by suggested between normal empty) observed 199]) give the complete bundle, provided that that examples of counter-examples is a c l o s e d that to that 1 ÷ ~X f Let f 1 ~X/Y is s u r j e c t i v e . e. topology. The X theorem philosophy must to s t u d y here sin- is t h a t occur. be a c o m p l e t e be an u n r a m i f i e d : X + Y variety morphism. f is u n r a m i f i e d is zero. is u n r a m i f i e d that connectedness Space. of d i m e n s i o n If 2n > m , embedding.