Related papers: On intrinsic quadrics

We show that the reduced motive of a smooth affine quadric is invertible as an object of the triangulated category of motives DM(k, ZZ[1/e]) (where k is a perfect field of exponential characteristic e). We also establish a motivic version…

Let $S$ be a smooth del Pezzo surface over a field $k$ of characteristic $\neq 2, 3$. We define an invariant in the Grothendieck-Witt ring $GW(k)$ for "counting" rational curves in a curve class $D$ of fixed positive degree (with respect to…

A quadratic invariant is defined as a quadratic form in the elements of a tensor that remains invariant under a group of coordinate transformations. It is proved that there are 7 quadratic invariants of the 21-element elastic modulus tensor…

In this paper we characterize smooth complex projective varieties that admit a quadric bundle structure on some dense open subset in terms of the geometry of certain families of rational curves.

A symplectic manifold is called symplectic rationally connected if there is a non-zero genus zero Gromov-Witten invariant with two point insertions. It is conjectured that every smooth projective rationally connected variety is symplectic…

Intrinsic volumes, which generalize both Euler characteristic and Lebesgue volume, are important properties of $d$-dimensional sets. A random cubical complex is a union of unit cubes, each with vertices on a regular cubic lattice,…

In this paper we classify and derive closed formulas for geometric elements of quadrics in rational B\'ezier triangular form (such as the center, the conic at infinity, the vertex and the axis of paraboloids and the principal planes), using…

We prove a version of Manin's conjecture for a certain family of intrinsic quadrics, the base field being a global field of positive characteristic. We also explain how a very slight variation of the method we use allows to establish the…

An abstract indefinite least squares problem with a quadratic constraint is considered. This is a quadratic programming problem with one quadratic equality constraint, where neither the objective nor the constraint are convex functions.…

We determine the Cox rings of the minimal resolutions of cubic surfaces with at most rational double points, of blow ups of the projective plane at non-general configurations of six points and of three dimensional smooth Fano varieties of…

We give a fermionic Fock space description of embedded entangled qubits. Within this framework the problem of classification of pure state entanglement boils down to the problem of classifying spinors. The usual notion of separable states…

Orthostochastic matrices are the entrywise squares of orthogonal matrices, and naturally arise in various contexts, including notably definite symmetric determinantal representations of real polynomials. However, defining equations for the…

For $n\geq 4$, let $X$ be a complex smooth Fano $n$-fold whose minimal anticanonical degree of non-free rational curves on $X$ is at least $n-2$. We classify extremal contractions of such varieties. As an application, we obtain a…

For each real quadratic field we constructively show the existence of infinitely many exceptional quartic number fields containing that quadratic field. On the other hand, another infinite collection of quartic exceptional fields without…

We consider intrinsic square functions defined using (log-)Dini continuous test functions on spaces of homogeneous type. We prove weighted estimates with optimal (at least in the Euclidean case) dependence on the aperture of the cone used…

Assuming an integral quadratic polynomial with nonsingular quadratic part has a nontrivial zero on an integer lattice outside of a union of finite-index sublattices, we prove that there exists such a zero of bounded norm and provide an…

For every positive integer k, it is shown that there exists a positive definite diagonal quaternary integral quadratic form that represents all positive integers except for precisely those which lie in k arithmetic progressions. For k=1,…

We describe convex quadric surfaces in n dimensions and characterize them as convex surfaces with quadric sections by a continuous family of hyperplanes.

We characterize positive definiteness for some family of matrices. As an application we derive explicit value of the quadratic embedding constants of the path graphs.

A bivariate quartic form is a homogeneous bivariate polynomial of degree four. A criterion of positivity for such a form is known. In the present paper this criterion is reformulated in terms of pseudotensorial invariants of the form.