Results 51 to 60 of about 25,625 (190)

Computing isogenies between Jacobian of curves of genus 2 and 3 [PDF]

, 2019
We present a quasi-linear algorithm to compute isogenies between Jacobians of curves of genus 2 and 3 starting from the equation of the curve and a maximal isotropic subgroup of the l-torsion, for l an odd prime number, generalizing the V\'elu's formula ...
Milio, Enea
core   +2 more sources

Hyperelliptic Jacobians and isogenies

, 2018
Motivated by results of Mestre and Voisin, in this note we mainly consider abelian varieties isogenous to hyperelliptic Jacobians In the first part we prove that a very general hyperelliptic Jacobian of genus $g\ge 4$ is not isogenous to a non ...
Naranjo, Juan Carlos, Pirola, Gian Pietro   +1 more
core   +1 more source

Fast genus 2 arithmetic based on Theta functions

Journal of Mathematical Cryptology, 2007
In 1986, D. V. Chudnovsky and G. V. Chudnovsky proposed to use formulae coming from Theta functions for the arithmetic in Jacobians of genus 2 curves.
Gaudry P.
doaj   +1 more source

MODULAR BUNDLE ADJUSTMENT FOR PHOTOGRAMMETRIC COMPUTATIONS [PDF]

The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 2018
In this paper we investigate how the residuals in bundle adjustment can be split into a composition of simple functions. According to the chain rule, the Jacobian (linearisation) of the residual can be formed as a product of the Jacobians of the ...
N. Börlin, A. Murtiyoso, P. Grussenmeyer, F. Menna, E. Nocerino   +4 more
doaj   +1 more source

Tropical Jacobians in R2 [PDF]

, 2010
By tropical Abel-Jacobi theorem, the Jacobian of a tropical curve is isomorphic to the Picard group. A tropical curve in $\mathbb{R}^2$ corresponds to an immersion from a tropical curve to $\mathbb{R}^2$. In this paper, we show that any principal divisor
Yoshitomi, Shuhei
core   +2 more sources

Del Pezzo surfaces of degree 1 and jacobians

, 2006
We construct absolutely simple jacobians of non-hyperelliptic genus 4 curves, using Del Pezzo surfaces of degree 1.
A. Elkin, A. Silverberg, B. Mortimer, Ch. Jansen, D. Mumford, D. Mumford, D.S. Passman, F. Oort, I.R. Shafarevich, J.-P. Serre, J.-P. Serre, J.H. Conway, N. Bourbaki, P.B. Kleidman, R. Erné, R. Hartshorne, V.A. Iskovskikh, V.A. Iskovskikh, W. Feit, Y.G. Zarhin, Y.G. Zarhin, Y.G. Zarhin, Y.G. Zarhin, Y.I. Manin, Y.I. Manin, Y.I. Manin, Yu. G. Zarhin   +26 more
core   +5 more sources

The arithmetic of genus two curves with (4,4)-split Jacobians

, 2011
In this paper we study genus 2 curves whose Jacobians admit a polarized (4,4)-isogeny to a product of elliptic curves. We consider base fields of characteristic different from 2 and 3, which we do not assume to be algebraically closed.
Bolza, Bosma, Donagi, Frey, Frey, Gaudry, Igusa, Igusa, J.-B., Kani, Kani, Kevin Doerksen, Krazer, Kuhn, L.-C., Magaard, Milne, Murabayashi, Nils Bruin, Shaska, Shaska, Silverberg   +21 more
core   +1 more source

The minimum and maximum number of rational points on jacobian surfaces over finite fields

, 2010
We give some bounds on the numbers of rational points on abelian varieties and jacobians varieties over finite fields. The main result is that we determine the maximum and minimum number of rational points on jacobians varieties of dimension ...
Haloui, Safia
core   +2 more sources

Weil descent of Jacobians

Discrete Applied Mathematics, 2001
The paper considers Weil restrictions as a means to solve the discrete logarithm problem in elliptic curves. In particular, it considers the Jacobian of a genus \(g>1\) curve \(C\) over a finite field \(\mathbb{F}_{q^n}\), where \(q\) is a prime and \(n>1\).
openaire   +1 more source

Generalized Quasi-Static Mooring System Modeling with Analytic Jacobians

Energies
This paper presents a generalized and efficient method for quasi-static analysis of mooring systems, including complex scenarios such as when shared mooring lines interconnect multiple floating wind or wave energy devices.
Matthew Hall
doaj   +1 more source