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

ISBN-10: 3540108335

ISBN-13: 9783540108337

ISBN-10: 354038720X

ISBN-13: 9783540387206

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

Example text

Jouanolou, letter from communi- S. Bloch, H. Hamm, in notes. and the have b e n i f i t t e d R. Mandelbaum, D. Prill, variety. that to circulated in the p r e s e n t M. Artin, K. Johnson, were from Deligne, P. Griffiths, R. M a c P h e r s o n , C. i. and u p d a t e d its p r e s e n t a t i o n R. Hartshorne, L~ D~ng-Tr~ng, for the e x t e n s i o n s of sections correspondence cation w i t h m a n y others, J. Harris, of a number revised the crucial N. Goldstein, indicated fields. Preliminary [17].

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. As which We p r e emphasizes fundamental group algebraic covering of of A b h y a n k a r of e v e r y case, reduces component of theorem.

F : X + ~m and in a morphism. 1. is (unibranch in the it is irreducible. we assume a variety is locally irreducible, Bertini; ~ The simplest way of a r r a n g i n g this is to require that be locally i r r e d u c i b l e in the classical irreducible, is irreducible. f-l(L) space. Fix Then there is a n o n - e m p t y Z a r i s k i - o p e n set such that for all is irreducible; (m- d) - planes L i_nn U : 34 (B) Z l (f-i (L)) Proof. ally We will make finite-to-one Note that Zariski-open fact that follows f CLAIM.

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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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