On certain properties of parametric curves.
نویسندگان
چکیده
منابع مشابه
On Certain Uniformity Properties of Curves over Function Fields
Arguing by induction on the dimension, it is easy to show that the same holds for higher dimensional base varieties, more precisely, let V be a smooth variety over C and let T be a closed subset of V . Define Fg(V, T ) as the set of non-isotrivial families of smooth curves of genus g ≥ 2 over V − T . Then Fg(V, T ) is finite. Partial motivation for the Shafarevich conjecture was that, as Parshi...
متن کاملOn the rank of certain parametrized elliptic curves
In this paper the family of elliptic curves over Q given by the equation Ep :Y2 = (X - p)3 + X3 + (X + p)3 where p is a prime number, is studied. Itis shown that the maximal rank of the elliptic curves is at most 3 and someconditions under which we have rank(Ep(Q)) = 0 or rank(Ep(Q)) = 1 orrank(Ep(Q))≥2 are given.
متن کاملConvexity Conditions of Planar Parametric Curves and its Properties
Based on the original geometrical definition of the planar parametric convex curve, the local convexity and the global convexity on parametric curve are discussed, a few properties are obtained, and a necessary and sufficient condition is presented for the local convexity of a general planar parametric curve.
متن کاملOn a characterization of certain maximal curves
where C(Fq) denotes the set of Fq-rational points of the curve C. Here we will be interested in maximal(resp. minimal) curves over Fq2 , that is, we will consider curves C attaining Hasse-Weil’s upper (resp. lower) bound: #C(Fq2) = q + 1 + 2gq (resp. q + 1− 2gq). Here we are interested to consider the hyperelliptic curve C given by the equation y = x + 1 over Fq2 . We are going to determine whe...
متن کاملon the rank of certain parametrized elliptic curves
in this paper the family of elliptic curves over q given by the equation ep :y2 = (x - p)3 + x3 + (x + p)3 where p is a prime number, is studied. itis shown that the maximal rank of the elliptic curves is at most 3 and someconditions under which we have rank(ep(q)) = 0 or rank(ep(q)) = 1 orrank(ep(q))≥2 are given.
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: Journal of the Mathematical Society of Japan
سال: 1960
ISSN: 0025-5645
DOI: 10.2969/jmsj/01220129