Curves of genus 2 with split jacobian
WebApr 17, 2024 · We will talk about the Ceresa class, which is the image under a cycle class map of a canonical homologically trivial algebraic cycle associated to a curve in its … WebConstructing Pairing-Friendly Genus 2 Curves with Split Jacobian 3 eties. In order to obtain pairing-friendly ordinary abelian surfaces, which generically have ˆ-value around …
Curves of genus 2 with split jacobian
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Webto have a split Jacobian for some curves Cin positive characteristic (see e.g. discussion in [2]). In particular, one can have a Jacobian of the form J(C) = E 1 E 2;the sum of two … WebJun 20, 2008 · In this article, we give a new proof of the existence of curves of genus 5 and 17 with split Jacobian by constructing explicit two families of such curves over number …
WebPrincipally polarised abelian varieties of dimension two which are isogenous over the rationals to a genus 2 Jacobian over the rationals by an isogeny of degree a power of two can be computed. ... ExceptionalDivisors returns all (-1)-curves (including irreducible curves that split into a conjugate set of (-1)-curves over a finite extension of ... WebSplit jacobian curves of genus 2 have also been used to exhibit nonisomorphic curves with the same jacobian; vide [3, 4]. The approach in these papers is through the algebraic geometry of abelian varieties, and the constructions are therefore far from explicit. …
WebJan 1, 2002 · Let C be a genus 2 curve defined over k, char (k)=0. If C has a (3,3)-split Jacobian then we show that the automorphism group Aut (C) is isomorphic to one of the … WebUsing genus 2 curves with simple but not absolutely simple Jacobians one can obtain pairing-based cryptosystems more efficient than for a generic genus 2 curve. We describe a new framework to construct pairing-friendly abelian surfaces, which are simple but not absolutely simple.
WebSplit jacobian curves of genus 2 have also been used to exhibit nonisomorphic curves with the same jacobian; vide [3, 4]. The approach in these papers is through the …
WebJul 25, 2008 · T. Shaska. Genus 2 curves with (3; 3)-split Jacobian and large automorphism group. In Algorithmic number theory (Sydney, 2002), volume 2369 of … msnbc free live streaming online newsWebEnter the email address you signed up with and we'll email you a reset link. msnbc free streaming live newsWebLARGE TORSION SUBGROUPS OF SPLIT JACOBIANS OF CURVES OF GENUS TWO OR THREE EVERETT W. HOWE, FRANCK LEPREVOST, AND BJORN POONEN´ … msnbc free streaming liveWebThe study of genus 2 curves with split Jacobian has a long history which arguably started with the task of reducing hyperelliptic integrals of genus 2 of the first kind to sums of elliptic integrals. Here a substitution of variables gives rise to a genus 2 cover of an elliptic curve. The study for degree 2 dates how to make gluten free biscuitsWebGenus 2 curves with given split Jacobian Jasper Scholten [email protected] November 22, 2024 Abstract Given 2 Elliptic Curves E 1 and E 2, we use some theory of elliptic Kummer surfaces to construct a hyperelliptic curve with Jacobian isogenous to E 1 E 2. We require the 2-torsion of E 1 and E 2 to be de ned over the eld we are working ... msnbc free live streaming tv onlineWebJan 1, 2002 · There are exactly six ℂ-isomorphism classes of genus two curves \mathcal {C} with Aut ( \mathcal {C} ) isomorphic to D 8 (resp., D 12) and with (3, 3)-split … msnbc free stream onlineWebDec 5, 2012 · Yuri Zarhin. 4,990 19 30. Add a comment. 4. Every curve of genus 2 has an equation of the form Y 2 Z 4 = f 0 X 6 + f 1 X 5 Z + ⋯ + f 6 Z 6. ] Flynn (1990) has found … how to make gluten free cheese curds