Now showing items 1-16 of 16

  • Hulek, Klaus; Ranestad, Kristian (Research report / Forskningsrapport, 1998)
  • Gustavsen, Trond Stølen; Ranestad, Kristian (Research report / Forskningsrapport, 2004)
    Given an ordinary elliptic curve on Hesse form over a finite field of characteristic three, we give a sequence of elliptic curves which leads to an effective construction of the canonical lift, and obtain an algorithm for ...
  • Blekherman, Grigoriy; Hauenstein, Jonathan; Ottem, John Christian; Ranestad, Kristian; Sturmfels, Bernd (Journal article / Tidsskriftartikkel / SubmittedVersion, 2012)
    We study the geometry underlying the difference between non-negative polynomials and sums of squares (SOS). The hypersurfaces that discriminate these two cones for ternary sextics and quaternary quartics are shown to be ...
  • Ranestad, Kristian; Sturmfels, Bernd; Amendola, Carlos (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2017)
    We prove that all moment varieties of univariate Gaussian mixtures have the expected dimension. Our approach rests on intersection theory and Terracini’s classification of defective surfaces. The analogous identifiability ...
  • Braun, Robert; Ranestad, Kristian (Research report / Forskningsrapport, 1993)
  • EPW Cubes 
    Iliev, Atanas; Kapustka, Grzegorz; Kapustka, Michal; Ranestad, Kristian (Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2016)
    We construct a new 20-dimensional family of projective six-dimensional irreducible holomorphic symplectic manifolds. The elements of this family are deformation equivalent with the Hilbert scheme of three points on a K3 ...
  • Ranestad, Kristian; Mezzetti, Emilia; De Poi, Pietro; Faenzi, Daniele (Journal article / Tidsskriftartikkel / PublishedVersion; Peer reviewed, 2017)
    We study congruences of lines Xω defined by a sufficiently general choice of an alternating 3-form ω in n dimensions, as Fano manifolds of index 3 and dimension n-1. These congruences include the G2-variety for n=6 and the ...
  • Ranestad, Kristian (Research report / Forskningsrapport, 1997)
  • Ranestad, Kristian; Kapustka, Michal; Kapustka, Grzegorz; Iliev, Atanas (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2017)
    We show that a Hilbert scheme of conics on a Fano fourfold double cover of P2×P2 ramified along a divisor of bidegree (2,2) admits a P1-fibration with base being a hyper-Kähler fourfold. We investigate the geometry of such ...
  • Iliev, Atanas; Ranestad, Kristian (Research report / Forskningsrapport, 1998)
  • Ranestad, Kristian; Bernardi, Alessandra; Jelisiejew, Joachim; Marques, Pedro Macias (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2017)
    Using Macaulay’s correspondence we study the family of Artinian Gorenstein local algebras with fixed symmetric Hilbert function decomposition. As an application we give a new lower bound for the dimension of cactus varieties ...
  • Ranestad, Kristian; Ottem, John Christian; Sturmfels, Bernd; Vinzant, Cynthia (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2014)
    Quartic spectrahedra in 3-space form a semialgebraic set of dimension 24. This set is stratified by the location of the ten nodes of the corresponding real quartic surface. There are twenty maximal strata, identified ...
  • Popescu, Sorin; Ranestad, Kristian (Research report / Forskningsrapport, 1993)
  • Aure, Alf; Decker, Wolfram; Hulek, Klaus; Popescu, Sorin; Ranestad, Kristian (Research report / Forskningsrapport, 1996)
  • Ranestad, Kristian; Gallet, Matteo; Villamizar, Nelly (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2018)
    Powersum varieties, also called varieties of sums of powers, have provided examples of interesting relations between varieties since their first appearance in the 19th century. One of the most useful tools to study them ...
  • Ranestad, Kristian; Voisin, Claire (Journal article / Tidsskriftartikkel / AcceptedVersion; Peer reviewed, 2017)
    We show that a cubic fourfold F that is apolar to a Veronese surface has the property that its variety of power sums V SP ( F, 10) is singular along a K 3 surface of genus 20 which is the variety of power sums of a sextic ...