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**

Stormes, B. Teissier, 50. Unless Notation, otherwise stated, The a s s e r t i o n ment it is non-empty. 2. 3. Given maps Y ×X Z that, denotes f : Y ÷ X the fibre Sommese, Facts. 4. A. D. Mumford, Zariski. the G r a s s m a n n i a n m-space A. Landman, and P r e l i m i n a r y a variety that a space denotes K. Saito, a n d O. Conventions, R. Hardt, B. Moishezon, J. Roberts, K. Vilonen, T. Gaffney, J. Hansen, J. P. Jouanolou, letter from communi- S. Bloch, H. Hamm, in notes. and the have b e n i f i t t e d R.

1 and : X n ÷ ~m cated by The the generalize fact the §7. degree In a r e c e n t X Hartshorne's Roberts' We of adopt projective Zak's x , T T work. the of maps m > n mathematician how it normality. Roberts to This and we Conjecture L. Zak tangent a proof section to a of is d e v o t e d independently suggested results, which F. spaces leads in refer indi- covering. Hartshorne's linear are notions a branched and arguments detailed it of Soviet J. his when different degrees linear finite Zak's the J.

Preliminary [17]. with references Any ×X Z = {(y,z) statement algebraically closed tions (B), labeled classical as the field, (A) refers and to the the ground one unless respectively labeled E Y × Z field otherwise "algebraic" is I f(y) to v a r i e t i e s Zariski over an a r b i t r a r y topology. In asser- ~ , and the t o p o l o g y indicated. and = g(z)} We will "topological" refer is the to these settings. 5. 6. with that and we are working locally covering path X that ~l(X,f(y)) this (i) induced structure, setting, defined if : X ÷ X denote analytic b y the f : Y + X the space, requirement that is a c o n t i n u o u s map, )~ z I (X) homomorphism is s u r j e c t i v e for s o m e of the choice y of f.