Algebraic Geometry: Proceedings of the Third Midwest by D. Burns (auth.), I. Dolgachev (eds.)

By D. Burns (auth.), I. Dolgachev (eds.)

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Read or Download Algebraic Geometry: Proceedings of the Third Midwest Algebraic Geometry Conference held at the University of Michigan, Ann Arbor, USA, November 14–15, 1981 PDF

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Extra info for Algebraic Geometry: Proceedings of the Third Midwest Algebraic Geometry Conference held at the University of Michigan, Ann Arbor, USA, November 14–15, 1981

Sample text

In fact, if since is the full symmetric group, transversal W - AI2 - A34 - Al4 - A23 = FI2 n F34 n F'14 n F'23, is transversal, eral, we consider the variety (3,3) in Q such that the above situa- in the linear system gives a transversal A c [0Q(3,3)] A = {(C, yl,Y2,Y3,Y4 ) I Yi ~ C, A has only ordinary p. e. 4, × Q4 i0Q(3,3)] intersection for C gen- defined by p(yl) = p(y2) , p(y3) = p(y4) , p'(y2 ) = p'(y3) , p'(yl ) = p'(y4)} is of dimension 15 and smooth at the general point, hence our assertion is proven if the projection of the case, for C A general, Finally we compute: on [0Q(3,3)] is surjective: FI2 n F34 n Frl4 n F'23 but if this were not would be empty.

Sup. Pis Serie IV, vo. VII, 1 (1981), 35-68. of the space of curve of given Ann. Sci. 1] sub- sDace. submani~olds, Z, N ( M ) , a trivial of of If T*Z. X let C c M Put should space 0X c T * Z l x Now, by a paper the G r a s s m a n n of A. e. 8], fN 3, b e l o w . set of bundle of talk was motivated who worked N*(X0). complex group, of a m p l e n e s s . This the C c M Lie of c o n s t r u c t i n g bundle the c o n o r m a l criterion open a compact a method the n o r m a l semisimple M N*(X) happen of X.

Proof. Let for any fixed U ~, be the set of all hyperplanes meeting 7rl(U,~ ) C transversally. operates as the full symmetric group on ~ Then n C. It follows that if we set ~ then ~i = [(Pl ..... p~,H) is irreducible I H e U, PieHNC] , [2]. Now F = [(Pl ..... c, b y hypothesis. is quasi-finite, we can choose the H. in HI , Since the map from not in the image of ~. ~@+3 Thus i #(R i n C) = r + 2. Now let H i, D be any curve of degree R i n D = ~. _< r in ]pr. We claim that for generic Indeed let F = [(Pl .....

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