Rational Families of Conics and Quadrics
نویسنده
چکیده
A surface generated by a one parameter family of conics c(t) is called conic surface. If c(t) can be described by rational functions, the generated conic surface is rational. An algorithm to construct real rational parametrizations for such surfaces and some examples will be given.
منابع مشابه
Rational Points on Pencils of Conics and Quadrics with Many Degenerate Fibres
For any pencil of conics or higher-dimensional quadrics over Q, with all degenerate fibres defined over Q, we show that the Brauer–Manin obstruction controls weak approximation. The proof is based on the Hasse principle and weak approximation for some special intersections of quadrics over Q, which is a consequence of recent advances in additive combinatorics.
متن کاملThe projective reconstruction of points, lines, quadrics, plane conics and degenerate quadrics using uncalibrated cameras
In this paper we present an algorithm for the simultaneous projective reconstruction of points, lines, quadrics, plane conics and degenerate quadrics using Bundle Adjustment. In contrast, most existing work on projective reconstruction focuses mainly on one type of primitive. Furthermore, for the reconstruction of quadrics (both full-rank and degenerate) and plane conics, a novel algorithm for ...
متن کاملFundamental Groups of Some Special Quadric Arrangements
Abstract. Continuing our work on the fundamental groups of conic-line arrangements [3], we obtain presentations of fundamental groups of the complements of three families of quadric arrangements in P. The first arrangement is a union of n conics, which are tangent to each other at two common points. The second arrangement is composed of n quadrics which are tangent to each other at one common p...
متن کاملArithmetic Progressions on Conics.
In this paper, we look at long arithmetic progressions on conics. By an arithmetic progression on a curve, we mean the existence of rational points on the curve whose x-coordinates are in arithmetic progression. We revisit arithmetic progressions on the unit circle, constructing 3-term progressions of points in the first quadrant containing an arbitrary rational point on the unit circle. We als...
متن کاملBirational geometry of quadrics in characteristic 2
The theory of quadratic forms can be regarded as studying an important special case of the general problem of birational classification of algebraic varieties. A typical example of a Fano fibration in minimal model theory is a quadric bundle, which can be viewed without loss of information as a quadric hypersurface over the function field of the base variety. This description feeds the problem ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1998