منابع مشابه
Jacobian of Meromorphic Curves*
The contact structure of two meromorphic curves gives a factorization of their jacobian. Section 1: Introduction Let J(F,G) = J(X,Y )(F,G) be the jacobian of F = F (X,Y ) and G = G(X,Y ) with respect to X and Y , i.e., let J(F,G) = FXGY − FY GX where subscripts denote partial derivatives. Here, to begin with, F and G are plane curves, i.e., polynomials in X and Y over an algebraically closed gr...
متن کاملGeneralized Jacobian and Discrete Logarithm Problem on Elliptic Curves
Let E be an elliptic curve over the finite field F_{q}, P a point in E(F_{q}) of order n, and Q a point in the group generated by P. The discrete logarithm problem on E is to find the number k such that Q = kP. In this paper we reduce the discrete logarithm problem on E[n] to the discrete logarithm on the group F*_{q} , the multiplicative group of nonzero elements of Fq, in the case where n | q...
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A singular flat geometry may be canonically assigned to a real algebraic curve Γ; namely, via analytic continuation of unit speed parameterization of the real locus ΓR. Globally, the metric ρ = |Q| = |q(z)|dzdz̄ is given by the meromorphic quadratic differential Q on Γ induced by the standard complex form dx + dy on C = {(x, y)}. By considering basic properties of Q, we show that the condition f...
متن کاملSeshadri Constants on Jacobian of Curves
We compute the Seshadri constants on the Jacobian of hyperelliptic curves, as well as of curves with genus three and four. For higher genus curves we conclude that if the Seshadri constants of their Jacobian are less than 2, then the curves must be hyperelliptic.
متن کاملCurves of Genus 2 with Split Jacobian
We say that an algebraic curve has split jacobian if its jacobian is isogenous to a product of elliptic curves. If X is a curve of genus 2, and /: X —► E a map from X to an elliptic curve, then X has split jacobian. It is not true that a complement to E in the jacobian of X is uniquely determined, but, under certain conditions, there is a canonical choice of elliptic curve E' and algebraic f:X—...
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ژورنال
عنوان ژورنال: Proceedings Mathematical Sciences
سال: 1999
ISSN: 0253-4142,0973-7685
DOI: 10.1007/bf02841532