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

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

ISBN-10: 3540123377

ISBN-13: 9783540123378

ISBN-10: 3540409718

ISBN-13: 9783540409717

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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

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1. 1. Let d so that H ~ C generically and choose elliptic curves are chosen 6enerically, a linear system without base points with sion It then any nine points of ~(E i n C) : 9. Further~ if then H, We E i n Ej = (ii) degree We choose the and nine points lie on a cubic curve. follows by a monodromy argument that for generic on a smooth cubic curve. H passing through the nine points. ~P10. The proof then proceeds as above. 1. since the generic line bundle with §3, we let ~r1 : C l ~ S 1 tinct points of f~g = r + 1 ]p1.

1 constructs a good C and of degree g' of genus hi(L)- 2k >_ h0(C,L) 0, d + ( r - l)k satisfying the g and and a line k - (r + 1). 1 is established. 2, we let sional family of elliptic curves and let and d O = 3. The proof of Proposition Vl : C1 -~ S1 Q1 be a nontrivial one dimen- be the zero section. 1. REFERENCES [1] P. Deligne and D. Mumford, The irreducibility genus. Publ. IHES 36 (1969), 75-109. [el J. Harris, A bound on the geometric genus of projective varieties. Norm. Sup. Pis Serie IV, vo.

Zx~+TZ. Z curve CO. z 6 CO, Let g be d e f i n e d by the w e l l - k n o w n with ample. ~> gz. determines of for e a c h follows. z*:G + Z in at [8]. some is n o t A, map be the 62 Dualizing, we obtain T*Z Finally, project onto the 2 nd ÷ Z × g* factor. ~:T*Z T*Z + g* 9 a ~> ¢(a) = z #*(a) Z Remark. V = Let Np c Q (G × N p ) / P , be the n i l p o t e n t where P acts on p" (g,x) Let ~:V + G be d e f i n e d by G = radical ~ Np of P, and put by (gp-l,Ad(p) (x)). [g,x] ~> Ad(g) (x) .

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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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