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

**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 .....