An algorithm for constructing a basis of a linear system L(D) on a hyperelliptic curve is described. Algorithms by Cantor and Chebychev for computing in the Jacobian of a hyperelliptic curve are derived as special cases. The final section describes Chebychev's application of his algorithm to element
On the Intersections of Systems of Curves
โ Scribed by Gelasio Salazar
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 85 KB
- Volume
- 75
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
โฆ Synopsis
We show that the minimum number i m (n) of intersections in an n-family of simple closed curves whose elements pairwise intersect at least once and in less than m points satisfies the asymptotic behavior lim n ร i m (n)ร( n 2 )=2.
๐ SIMILAR VOLUMES
We find bounds for the genus of a curve over a field of characteristic p under the hypothesis that the Cartier operator of this curve has low rank and in the case where it is nilpotent. แฎ 2001 Academic Press c w x e.g., 11 . Moreover, we wish to remark that the rank of the Cartier operator on a curv
Let J R (v) denote the set of all integers k such that there exists a pair of KTS(v) with precisely k triples in common. In this article we determine the set J R (v) for v#3 (mod 6) (only 10 cases are left undecided for v=15, 21, 27, 33, 39) and establish that J R (v)=I(v) for v#3 (mod 6) and v 45,
A family of r sets is called a 2-system if any two sets have the same intersection. Denote by F(n, r) the most number of subsets of an n-element set which do not contain a 2-system consisting of r sets. Constructive new lower bounds for F(n, r) are given which improve known probabilistic results, an
## Abstract We study coherent systems on an irreducible nodal curve of arithmetic genus 1. We determine conditions for their nonโemptiness and study properties like irreducibility, smoothness, seminormality and rationality.