HYPERBOLIC ORDINARINESS OF HYPERELLIPTIC CURVES OF LOWER GENUS IN CHARACTERISTIC THREE
نویسندگان
چکیده
منابع مشابه
Maximal hyperelliptic curves of genus three
Article history: Received 24 June 2008 Revised 29 January 2009 Available online 27 February 2009 Communicated by H. Stichtenoth This note contains general remarks concerning finite fields over which a so-called maximal, hyperelliptic curve of genus 3 exists. Moreover, the geometry of some specific hyperelliptic curves of genus 3 arising as quotients of Fermat curves, is studied. In particular, ...
متن کاملNon-hyperelliptic curves of genus three over finite fields of characteristic two
Let k be a finite field of even characteristic. We obtain in this paper a complete classification, up to k-isomorphism, of non singular quartic plane curves defined over k. We find explicit rational normal models and we give closed formulas for the total number of k-isomorphism classes. We deduce from these computations the number of k-rational points of the different strata by the Newton polyg...
متن کاملGenerating Genus Two Hyperelliptic Curves over Large Characteristic Finite Fields
In hyperelliptic curve cryptography, finding a suitable hyperelliptic curve is an important fundamental problem. One of necessary conditions is that the order of its Jacobian is a product of a large prime number and a small number. In the paper, we give a probabilistic polynomial time algorithm to test whether the Jacobian of the given hyperelliptic curve of the form Y 2 = X+uX+vX satisfies the...
متن کاملHyperelliptic Curves in Characteristic 2
In this paper we prove that there are no hyperelliptic supersingular curves of genus 2n − 1 in characteristic 2 for any integer n ≥ 2. Let F be an algebraically closed field of characteristic 2, and let g be a positive integer. Write h = blog2(g + 1) + 1c, where b c denotes the greatest integer less than or equal to a given real number. Let X be a hyperelliptic curve over F of genus g ≥ 3 of 2-...
متن کاملThe modular variety of hyperelliptic curves of genus three
The modular variety of non singular and complete hyperelliptic curves with level-two structure of genus 3 is a 5-dimensional quasi projective variety which admits several standard compactifications. The first one comes from the period map, which realizes this variety as a sub-variety of the Siegel modular variety of level two and genus three H3/Γ3[2]. We denote the hyperelliptic locus by I3[2] ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Kyushu Journal of Mathematics
سال: 2019
ISSN: 1340-6116,1883-2032
DOI: 10.2206/kyushujm.73.317