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

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Additional 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

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Plr(t) .... ,Sk). ~a : ~t -~ ~ r If defined up to projective ha is very ample, we equivalence. 1. ,$a(Pi~). 2. ,~a(Pi~) lie in a hyperplane Hi H.. 1 a e Ar is 6ood. Then a is an isolated component of i__nn A r. y-l(~(a)) Proof. The set of y(a) = ~ b ) and ~ Thus we may choose b Sa common component. in Ar so that is very ample. ~b so that Sa(2p(a)) Sa(Pij) = ~b(P~j), 2p(a) and is very ample is open. Suppose Then HO(2p(a),~a ) = HO(2p(b),~b) ~ HO(c,L). 2~b ) and for ~b(~p(b)) have j = i ..... r, regarded as elements of C where C.

M4 the rational has covering s Proof. 21. D. by the automorphism IG'I/s = B(U)/s is with of degree point of variety. 48 which IG'I/s is a curve of genus More precisely, factors corresponds 4, R through to the is a rectangle in- R. the triple give isomorphic is either map of that (~,~)). o ({0,~} × ~I) g induced by a rational we associate g(~,~) of the rational 24 is a covering where C ~ IG'I such that R = (~I x {0,~}) then this paragraph and a general u ({0,~}×~]), IG'I It is then obvious is a vertex of Assume now that g c Aut(Q) tNe action on of degree IG'I + M 4 on datum of a triple into by = (y,x).

63(1981), 433-465. Catanese, F. Alg. 23(1982), 1-12. : Double solids, Advances in Mathematics, to appear. Publ. S. 10 (1929) (reprint 1961). : The unirationality of A 5, to appear. Harris, J. 67, I(1982) 23-86. : Arithmetic variety of moduli for genus two, Annals of Math. 72(1960), 612-649. : The uniruledness of MII , to appear. : Geometric invariant theory, Springer Verlag (I~65). E. Varenna, 1969, Cremonese. : Prym varieties I, in "Contributions to Analysis", Academic Press (1974), 325-350. : La variedad de los modulos de curvas de genero 4 es unirracional, Ann.

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