Tropical hyperelliptic curves in the plane
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Algebraic Combinatorics"
DOI: 10.1007/s10801-019-00933-3
Abstract: Abstractly, tropical hyperelliptic curves are metric graphs that admit a two-to-one harmonic morphism to a tree. They also appear as embedded tropical curves in the plane arising from triangulations of polygons with all interior lattice… read more here.
Keywords: curves plane; tropical hyperelliptic; hyperelliptic curves;
Computing twists of hyperelliptic curves
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Algebra"
DOI: 10.1016/j.jalgebra.2018.08.035
Abstract: Abstract We give an efficient algorithm to compute equations of twists of hyperelliptic curves C of arbitrary genus over any perfect field k (of characteristic different from 2) starting with a cocycle in H 1… read more here.
Keywords: computing twists; hyperelliptic curves; twists hyperelliptic;
On the sections of universal hyperelliptic curves
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Algebra"
DOI: 10.1016/j.jalgebra.2019.05.023
Abstract: In this paper, we will give an algebraic proof for determining the sections for the universal pointed hyperelliptic curves, when $g\geq 3$ and the image of the $\ell$-adic cyclotomic character $G_k\to \Z^\times$ is infinite. Furthermore,… read more here.
Keywords: hyperelliptic curves; sections universal; universal hyperelliptic;
Ranks of rational points of the Jacobian varieties of hyperelliptic curves
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Number Theory"
DOI: 10.1016/j.jnt.2018.08.002
Abstract: Abstract In this paper, we obtain bounds for the Mordell–Weil ranks over certain Z p -extensions (including cyclotomic Z p -extensions) of a wide range of abelian varieties defined over a number field F whose… read more here.
Keywords: hyperelliptic curves; points jacobian; jacobian varieties; rational points ... See more keywords
On certain maximal hyperelliptic curves related to Chebyshev polynomials
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Number Theory"
DOI: 10.1016/j.jnt.2019.03.003
Abstract: We study hyperelliptic curves arising from Chebyshev polynomials. The aim of this paper is to characterize the pairs $(q,d)$ such that the hyperelliptic curve $\cC$ over a finite field $\FF_{q^2}$ corresponding to the equation $y^2… read more here.
Keywords: hyperelliptic curves; curves related; related chebyshev; maximal hyperelliptic ... See more keywords
Divisor Class Halving Algorithms for Genus Three Hyperelliptic Curves
Sign Up to like & getrecommendations! Published in 2020 at "Chinese Journal of Electronics"
DOI: 10.1049/cje.2019.10.005
Abstract: In an (hyper)elliptic curve cryptosystem, the most important operation or the most time-consuming operation is the divisor scalar multiplication which consists of a sequence of doubling (of divisor) and addition (of two divisors). Point halving… read more here.
Keywords: curve cryptosystem; hyperelliptic curves; algorithms genus; halving algorithms ... See more keywords
2-Weierstrass points of genus 3 hyperelliptic curves with extra involutions
Sign Up to like & getrecommendations! Published in 2017 at "Communications in Algebra"
DOI: 10.1080/00927872.2016.1226861
Abstract: ABSTRACT We consider families of curves with extra automorphisms in ℋ3, the moduli space of smooth hyperelliptic curves of genus g = 3. Such families of curves are explicitly determined in terms of the absolute… read more here.
Keywords: weierstrass points; curves extra; points genus; genus hyperelliptic ... See more keywords
Numerical Verification of the Birch and Swinnerton-Dyer Conjecture for Hyperelliptic Curves of Higher Genus over ℚ up to Squares
Sign Up to like & getrecommendations! Published in 2019 at "Experimental Mathematics"
DOI: 10.1080/10586458.2019.1592035
Abstract: The Birch and Swinnerton-Dyer conjecture has been numerically verified for the Jacobians of 32 modular hyperelliptic curves of genus 2 by Flynn, Lepr\'evost, Schaefer, Stein, Stoll and Wetherell, using modular methods. In the calculation of… read more here.
Keywords: hyperelliptic curves; swinnerton dyer; dyer conjecture; birch swinnerton ... See more keywords
Rosenhain-Thomae formulae for higher genera hyperelliptic curves
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Nonlinear Mathematical Physics"
DOI: 10.1080/14029251.2018.1440744
Abstract: Rosenhain's famous formula expresses the periods of first kind integrals of genus two hyperelliptic curves in terms of θ-constants. In this paper we generalize the Rosenhain formula to higher genera hyperelliptic curves by means of… read more here.
Keywords: thomae formulae; rosenhain thomae; hyperelliptic curves; genera hyperelliptic ... See more keywords
On different expressions for invariants of hyperelliptic curves of genus 3
Sign Up to like & getrecommendations! Published in 2021 at "Journal of the Mathematical Society of Japan"
DOI: 10.2969/jmsj/83418341
Abstract: In this paper we give a passage formula between different invariants of genus 3 hyperelliptic curves: in particular between Tsuyumine and Shioda invariants. This is needed to get modular expressions for Shioda invariants, that is,… read more here.
Keywords: different expressions; expressions invariants; genus hyperelliptic; invariants hyperelliptic ... See more keywords