By Audun Holme, Robert Speiser
This quantity provides chosen papers caused by the assembly at Sundance on enumerative algebraic geometry. The papers are unique study articles and focus on the underlying geometry of the subject.
Read Online or Download Algebraic Geometry Sundance 1986: Proceedings of a Conference held at Sundance, Utah, August 12–19, 1986 PDF
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Extra info for Algebraic Geometry Sundance 1986: Proceedings of a Conference held at Sundance, Utah, August 12–19, 1986
Ms+i), j J ... That these two spaces are distinct follows from fact that the nodes of C impose independent conditions on curves of degree d - 3 and the monotonicity of Hilbert functions; this verifies the m u l t i p l i c i t y given for r(NL) in the s t a t e m e n t of t h e 34 Theorem. 4) of § i to express A, B, C, and A as linear combinations of CU, TN, TR and NL. 5) can be used to c o m p u t e the image u n d e r r of a n y class in the span of A, B, C and A. This includes most of the geometric divisor classes studied in this paper.
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. This gives a f a m i l y of plane c u r v e s of degree 4 m - III and genus 2. In a m a n n e r similar to Family Three we find that: ¢O = 5 H - 5E 0 : E l - . , . - E12 deE(A) = m 2 - III deE(B) = Sin- 111 deE(C) = 46 and deE(A) = 20.
4) L e m m a . by s c2; and t h a t these two c u r v e s In t h e deformation space of a triple point x 2 y + x y 2 + tlxY+ t2x+ t3Y+ t4 = 0 t h e f o l l o w i n g loci m a y be described as follows: t h e locus of c u r v e s w i t h t h r e e nodes m a y be given p a r a m e t r i c a l l y b y t I = c, t 2 = t 3-- t 4 = 0 or in Cartesian f o r m by the equations t 2 = 0, t 3 = 0, t 4 = 0; t h e locus of c u r v e s w i t h a t a c n o d e has t h r e e b r a n c h e s , g i v e n p a r a m e t r i c a l l y 1.