Effective Hasse principle for the intersection of two quadrics
نویسنده
چکیده
We consider a smooth system of two homogeneous quadratic equations over Q in n > 13 variables. In this case, the Hasse principle is known to hold, thanks to the work of Mordell in 1959. The only local obstruction is over R. In this paper, we give an explicit algorithm to decide whether a nonzero rational solution exists and, if so, compute one.
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 کاملA Survey of Applications of the Circle Method to Rational Points
of adèlic points under the product topology? Can one count the points in X(k) of bounded height? In favourable circumstances, the Hardy–Littlewood circle method can systematically provide answers to all of these questions. The focus of this survey will be upon the first and most basic of these questions: when is X(k) 6= ∅ for a given variety X defined over k? In considering what the circle meth...
متن کاملContinuous detection of the variations of the intersection curve of two moving quadrics in 3-dimensional projective space
We propose a symbolic algorithm for detecting the variations in the topological and algebraic properties of the intersection curve of two moving quadrics in PR(real projective 3-space). The core of our algorithm computes all the instants when the intersection curve of two moving quadrics changes type using resultants and Jordan forms. These instants partition the time axis into intervals within...
متن کاملContributions au calcul géométrique effectif avec des objets courbes de faible degré. (Contributions to effective geometric computing with low-degree curved objects)
We present the first efficient algorithm for computing an exact parametric representationof the intersection of two quadrics in three-dimensional real space given by implicit equations withrational coefficients. The output functions parameterizing the intersection are rational functionswhenever it is possible, which is the case when the intersection is not a smooth quartic (for exam...
متن کاملComputing quadric surface intersections based on an analysis of plane cubic curves
Computing the intersection curve of two quadrics is a fundamental problem in computer graphics and solid modeling. We present an algebraic method for classifying and parameterizing the intersection curve of two quadric surfaces. The method is based on the observation that the intersection curve of two quadrics is birationally related to a plane cubic curve. In the method this plane cubic curve ...
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 2016