Related papers: Strong approximation for the intersection of two q…
This paper is devoted to presenting a new approach to determine the intersection of two quadrics based on the detailed analysis of its projection in the plane (the so called cutcurve) allowing to perform the corresponding lifting correctly.…
For a smooth curve $B$ over an algebraically closed field $k$, for every $B$-flat complete intersection $X_B$ in $B\times_{\text{Spec}\ k} \mathbb{P}^n_k$ of type $(d_1,\dots,d_c)$, if the Fano index is $\geq 2$ and if…
We study the complexity of multiplication of two elements in a finite field extension given by their coordinates in a normal basis. We show how to control this complexity using the arithmetic and geometry of algebraic curves.
I propose an approximation scheme for asymptotically free field theories combining both weak coupling and strong coupling series. The weak coupling expansion is used to integrate the high frequency modes and the resulting low energy…
To support exactly tracking a neutron moving along a given line segment through a CAD model with quadric surfaces, this paper considers the arithmetic precision required to compute the order of intersection points of two quadrics along the…
In this paper, we study weak approximation with Brauer--Manin obstruction with respect to extensions of number fields. For any nontrivial extension $L/K,$ assuming a conjecture of M. Stoll, we prove that there exists a $K$-threefold…
We study rationality constructions for smooth complete intersections of two quadrics over nonclosed fields. Over the real numbers, we establish a criterion for rationality in dimension four.
We classify quartic del Pezzo surface fibrations over the projective line via numerical invariants, giving explicit examples for small values of the invariants. For generic such fibrations, we describe explicitly the geometry of spaces of…
We model weak gravitational lensing of light by large-scale structure using ray tracing through N-body simulations. The method is described with particular attention paid to numerical convergence. We investigate some of the key…
The aim of this paper is to give an effective version of the Strong Artin Approximation Theorem for binomial equations. First we give an effective version of the Greenberg Approximation Theorem for polynomial equations, then using the…
This paper addresses the approximation of fractional harmonic maps. Besides a unit-length constraint, one has to tackle the difficulty of nonlocality. We establish weak compactness results for critical points of the fractional Dirichlet…
Weak similarities form a special class of mappings between semimetric spaces. Two semimetric spaces $X$ and $Y$ are weakly similar if there exists a weak similarity $\Phi\colon X\to Y$. We find a structural characteristic of finite…
We study del Pezzo surfaces of degree 1 of the form w^2 = z^3 + Ax^6 + By^6 in the weighted projective space P_k(1,1,2,3), where k is a perfect field of characteristic not 2 or 3 and A,B \in k^*. Over a number field, we exhibit an infinite…
We present some elementary ideas to prove the following Sylvester-Gallai type theorems involving incidences between points and lines in the planes over the complex numbers and quaternions. (1) Let A and B be finite sets of at least two…
Campana introduced a notion of Campana rational connectedness for Campana orbifolds. Given a Campana fibration over a complex curve, we prove that a version of weak approximation for Campana sections holds at places of good reduction when…
The authors demonstrate quadratic mixing of weak time harmonic electromagnetic fields applied to Superconducting Quantum Interference Filters, manufactured from high-$T_{\mathrm{c}}$ grain boundary Josephson junctions and operated in active…
A quadrisecant of a knot is a straight line intersecting the knot at four points. If a knot has finitely many quadrisecants, one can replace each subarc between two adjacent secant points by the line segment between them to get the…
We construct explicit easily implementable polynomial approximations of sufficiently high accuracy for locally constant functions on the union of disjoint segments. This problem has important applications in several areas of numerical…
We introduce a notion of a weak elementary fibration and prove that it does exist in certain interesting cases. Our notion is a modification of the M. Artin's notion of an elementary fibration.
We extend an exact sequence of Colliot-Thelene and Sansuc which connects arithmetic and birational invariants of tori over a number field to one for arbitrary connected linear algebraic groups.