Related papers: Some new rational Gushel fourfolds
In this paper we present some new upper bounds of the Cusa-Huygens and the Huygens approximations. Bounds are obtained in the forms of some polynomial and some rational functions.
We classify newforms with rational Fourier coefficients and complex multiplication for fixed weight up to twisting. Under the extended Riemann hypothesis for odd real Dirichlet characters, these newforms are finite in number. We produce…
We give counting formulas for the number of Fourier-Mukai partners of the K3 category of a very general special cubic fourfold.
We give description of rational solutions of polynomial-equations.
We present four types of infinitely many exactly solvable Fokker-Planck equations, which are related to the newly discovered exceptional orthogonal polynomials. They represent the deformed versions of the Rayleigh process and the Jacobi…
We exhibit new examples of rational cubic fourfolds, parametrized by a countably infinite union of codimension-two subvarieties in the moduli space. Our examples are fibered in sextic del Pezzo surfaces over the projective plane; they are…
We study the set of rational curves of a certain topological type in general members of certain families of Calabi-Yau threefolds. For some families we investigate to what extent it is possible to conclude that this set is finite. For other…
Basic facts and definitions of conformal moduli of rings and quadrilaterals are recalled. Some computational methods are reviewed. For the case of quadrilaterals with polygonal sides, some recent results are given. Some numerical…
We derive new algebraic equations for the folding angle relationships in completely general degree-four rigid-foldable origami vertices, including both Euclidean (developable) and non-Euclidean cases. These equations in turn lead to novel,…
We give several examples of pairs of non-isomorphic cubic fourfolds whose Fano varieties of lines are birationally equivalent (and in one example isomorphic). Two of our examples, which are special families of conjecturally irrational…
We perform a systematic study of Gushel-Mukai varieties---quadratic sections of linear sections of cones over the Grassmannian Gr(2,5). This class of varieties includes Clifford general curves of genus 6, Brill-Noether general polarized K3…
In this paper we introduce and study motives for rational homotopy types.
We survey some results on real rational surfaces focused on their topology and their birational geometry.
In this paper we give new identities involving q-Euler polynomials of higher order.
An updated determination of the parameters of the Cabibbo-Kobayashi-Maskawa matrix is presented.
We study Hilbert schemes of quadrics of dimension $k \in \{0,1,2,3\}$ on smooth Gushel-Mukai varieties $X$ of dimension $n \in \{2,3,4,5,6\}$ by relating them to the relative Hilbert schemes of linear subspaces of dimension $k + 1$ of a…
The aim of this paper is to study quasi-rational polygons related to the outer billiard. We compare different notions introduced, and make a synthesis of those.
We define a new family of valuations on polyhedral cones valued in the space of bounded polyhedra.
We introduce new obstructions to rationality for geometrically rational threefolds arising from the geometry of curves and their cycle maps.
We announce numerous new results in the theory of orthogonal polynomials on the unit circle.