Download Algebraic Geometry and Complex Analysis: Proceedings of the by George R. Kempf (auth.), Enrique Ramírez de Arellano (eds.) PDF

By George R. Kempf (auth.), Enrique Ramírez de Arellano (eds.)

From the contents:G.R. Kempf: The addition theorem for summary Theta functions.- L. Brambila: life of sure common extensions.- A. Del Centina, S. Recillas: On a estate of the Kummer kind and a relation among moduli areas of curves.- C. Gomez-Mont: On closed leaves of holomorphic foliations through curves (38 pp.).- G.R. Kempf: Fay's trisecant formula.- D. Mond, R. Pelikaan: becoming beliefs and a number of issues of analytic mappings (55 pp.).- F.O. Schreyer: sure Weierstrass issues occurr at such a lot as soon as on a curve.- R. Smith, H. Tapia-Recillas: The Gauss map on subvarieties of Jacobians of curves with gd2's.

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Extra resources for Algebraic Geometry and Complex Analysis: Proceedings of the Workshop held in Pátzcuaro, Michoacán, México, Aug. 10–14, 1987

Example text

6. (1) ---OE(U) Proof. From the diagram and the fact that ~ relation between Gauss if w e ) j(~) C ' J (C) is a l o c a l o ~ that , G = s o a' G: x" r~l* e'* seen in is i n j e c t i v e In o r d e r the morphism [acl* and map. 3) that a' ¢'*0E(U) ramified) the results of Beauville, i(~) ~ ~. 1. ® ~' the we need and so claim. 7. n*0H(1) ~ OE(U ® n). 8. Proof. ~'*(n*(0 the above Frorosition will follow from (i)) -~ ~X' Let us first observe volution, then j(g~) m': X' ~ IU G nl* ~ 2 that is m*(0 ~2(i)) = KX, - g~ .

So it follows that all planes ~*P/ + ~ * P in pass through e all Q~(~) has image the canonical Po: R ~ I~ C ~ aI* in 4 U P+i(P) one knows pE c I~C ® sI* i = i,... ~ = ~2(Pl + p2 ) , ~' = ~2(Pl +p2) , ~,' = ~2(Pl +p4) t h e n t h e rank Proof. C F. Consider now the rank interI~l * ] 4 quadric Q~(~) , a member of one 48 of the rulings ~*P3 + ~*P4 point is ~*PI + ~*P2 and a member of the other ruling is and both contain the line Vq(~(~)),F Vq(~(~,),F Therefore point and that Q~(~,,) all three quadrics F, Let of p.

Give rise The two lines of the tangent tangent F° . morphism exactly if and only F is the o D e n o t e by is a ~ l a n e ~uintic. e. and the p r o j e c t i v i z a t i o n [ model i~Fie = ~ 4 . of the net, at ~ost smooth, of the net throuch of the net, have L is a degree C). not triconal, quadrics of rank < 4 ii at a p o i n t rank ~ 4. there and genus 3 A C ~ the q u a d r i c s arithmetic W4(F) (as is of parametryzing discriminant tryzing 5 intersection the Tlane to locus of the Beauville's results.

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