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

ISBN-10: 3540123377

ISBN-13: 9783540123378

ISBN-10: 3540409718

ISBN-13: 9783540409717

**Read Online 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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**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**

**Sample text**

Pr+2 s e H0(C,L) To establish our second assertion we choose ~VL(~l ), .... ~v,(P9) is a generic hyperplane, of dimension d. Let V' is be are contained in a smooth cubic curve. Pr+3 ~ ~V '(C) in H V ~ ~(C,L) ~V : C -~ ~ r is ~eneric linear subspace dimen- h0(L) > 10, be a subspace of and If we let H. has only nodes and degree R q + 1 = h0(C,L). and if but nine points of all lie on a hyperplane V and be a very ample line bundle of dim V = r + l, is a ~eneric hyperplane in r = 3 L W = ~(C,L), h0(C,L) >_ r + 4 If in a cubic c u r v % Proof.

Vorlesungen uber Algebralschen Geometrie, Teubner, Leipzig (1921). Ann. 260, (1982) 317-350. : Untersuchungen ~ber Thetafunktionen, Teubner, Leipzig (1895) A CONSTRUCTION OF SPECIAL SPACE CURVES D. Gieseker* University of California Los Angeles, California 90024 §l. zero. We will work over a fixed algebraically closed field of characteristic A curve plane. i. If smooth curves of ~enus For r = 3, be positive integers, and let (r - 1) g, ~ , d' ~ (r + 3) + g' and de~ree d' r > 3 be an integer. then there are non-degenerate i__nn ]pr.

We obtain a rational to the pair domi- [C,(oo,~)]. then there exists fixed and such that are induced, M (I,~)}. {~} × ~I are isomorphic: leaves ]pl × ]pl M4, I. to have chosen IG[ = IIM(3,3) I e IGI on (0,~) be the ideal just by sending to Le the point (~,i), an g(C) = C', via the Segre embedding, A = (]pl × {~}) u ({co} × ]pl) = rs = g2' M4, 1 coordinates such that then 2r We can thus reformulate Theorem (3,3) and that the two lines (x,y) by the involution gl' g2 r3= g3gl: sr of bidegree and let ]pl0 is not hyperelliptic by invariant, and, since g(M) = M.

### Algebraic Geometry: Proceedings of the Third Midwest Algebraic Geometry Conference held at the University of Michigan, Ann Arbor, USA, November 14–15, 1981 by D. Burns (auth.), I. Dolgachev (eds.)

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