Download Algebraic Geometry Sundance 1986: Proceedings of a by Audun Holme, Robert Speiser PDF

By Audun Holme, Robert Speiser

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

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Additional info for Algebraic Geometry Sundance 1986: Proceedings of a Conference held at Sundance, Utah, August 12–19, 1986

Example text

C and hence that C = 0 and B = - A . B A. References [D] S. S. 56 (1985) [D-HI] S. 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.

Ps÷l be the nodes of a c u r v e C e V(d,8+l); let Ill i be t h e m a x i m a l ideal of Pi in ~2, Li a line t h r o u g h Pl a n d ~ the e q u a t i o n of t h e line t h r o u g h Pi polar to Ll w i t h respect to t h e b r a n c h e s of C a t Pi. Then t h e t a n g e n t space to V (d, 8+1) a t q (the point of ~N corresponding to C) is the space of sections HO(c, (So(d)® r o t ® ... ®ms+i), while t h e t a n g e n t space to a b r a n c h of N L a t q corresponding to s m o o t h i n g and keeping a node on Lj , i ~ j, is the space of sections HO(c, @c(d) ® m i ® ®fni® .

F r o m the dimension calculations of [D-HI] we also see t h a t t h e general fiber of this f a m i l y is nonsingular a n d t h e singular fibers e a c h h a v e only one simple node as a singularity. Let I be a subset of {I, 2 . . . 12} containing a t m o s t 3 elements; again, denote b y III t h e n u m b e r of e l e m e n t s in I. H - ~E 1 i~l 39 w h e r e m_> 1 and I = ~ if m = 1; as in the previous case m a p X to projective space using the linear s y s t e m IDI and take a generic projection to p2.

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