By Holme R. Speiser (Eds.)

ISBN-10: 3540192360

ISBN-13: 9783540192367

This quantity offers chosen papers as a result of the assembly at Sundance on enumerative algebraic geometry. The papers are unique study articles and focus on the underlying geometry of the topic.

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**Additional info for Algebraic Geometry Sundance 1986**

**Example text**

Q 2 - i ~ I E i to p r o j e c t i v e space u s i n g t h e l i n e a r s y s t e m IDI, t h e n t a k e a g e n e r i c projection of the image to p 2 This will give a f a m i l y of plane c u r v e s of degree 2a+Sb-lll and genus 2. q 2 - deE(A) = 2 a b - t l I deE(B) = 4b- 2 a - III ~ E. i I= 1 40 deg(C) = 28 deg(A) = 20. The proof of independence n o w follows i m m e d i a t e l y f r o m the existence of these families. Specifically, to show a) a b o v e use families i and 2; for b) use families 1, 2 and 3; for c) use families 1, 2, 4 and 5 a n d for d) use families i a n d 4.

Diaz and J. Harris, Geometry of the Seven variety, preprint [D-H2] S. Diaz and J. Harris, Ideals associated to deformations of singular plane curves, preprint IF] W. eme-theoretic versus homogeneous generation of ideals Lawrence FAn, David Elsenbud, and b-~heldon Katz* Conten~ Positive results 1) C u r ~ on rational normal scrolls 2) Curves m Pq and p5 (Counter-) Examples 3) Deccerminantal constructions 't) General sets of points 5) Elliptic octic curves in p5 Summary In this note we consider cases in which a c u r v e in p r which is scheme theoretically the intersection of quadrics necessarily has homogeneous ideal generated by quadrics.

A node such t h a t the t a n g e n t line to one of the b r a n c h e s has c o n t a c t order t h r e e or m o r e with t h a t branch The divisor ]TB of c u r v e s with a flex bitangent - - t h a t is, a bitangent line h a v i n g c o n t a c t of o r d e r t h r e e o r m o r e w : t h the c u r v e at one of its points of tangency the divisor NL of c u r v e s with a node located s o m e w h e r e on a fixed line L c ~2 and m a n y others described in [D-HI]. We can also define divisors on C as well: for example, the divisor N of points of C lying over assigned nodes of the corresponding plane curves, and the divisor F of points lying over flexes.

### Algebraic Geometry Sundance 1986 by Holme R. Speiser (Eds.)

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