53 citations · 273 across the 39 of their papers we have counts for
32 papers · 1 filter
Non-general type surfaces in P4, an update
Hirotachi Abo, Kristian Ranestad, Frank-Olaf Schreyer
A general algebraic surface cannot be embedded in P4. Proving a conjecture by Hartshorne and Lichtenbaum, Ellingsrud and Peskine showed that there is a degree bound for smooth rati…
The variety of polar simplices II
Joachim Jelisiejew, Kristian Ranestad, Frank-Olaf Schreyer
We discuss the space of ideals with Hilbert function that are apolar to a full rank quadric . We prove that its components of saturated ideals are…
Convex hulls of surfaces in fourspace
Chiara Meroni, Kristian Ranestad, Rainer Sinn
This is a case study of the algebraic boundary of convex hulls of varieties. We focus on surfaces in fourspace to showcase new geometric phenomena that neither curves nor hypersurf…
Critical Curvature of Algebraic Surfaces in Three-Space
Paul Breiding, Kristian Ranestad, Madeleine Weinstein
We study the curvature of a smooth algebraic surface of degree from the point of view of algebraic geometry. More precisely, we consider umbilical points…
Adjoints and Canonical Forms of Polypols
Kathlén Kohn, Ragni Piene, Kristian Ranestad +5
Polypols are natural generalizations of polytopes, with boundaries given by nonlinear algebraic hypersurfaces. We describe polypols in the plane and in 3-space that admit a unique…
Twenty-Seven Questions about the Cubic Surface
Kristian Ranestad, Bernd Sturmfels
We present a collection of research questions on cubic surfaces in 3-space. These questions inspired a collection of papers to be published in a special issue of the journal Le Mat…
Projective geometry of Wachspress coordinates
Kathlén Kohn, Kristian Ranestad
We show that there is a unique hypersurface of minimal degree passing through the non-faces of a polytope which is defined by a simple hyperplane arrangement. This generalizes the…
Voronoi Cells of Varieties
Diego Cifuentes, Kristian Ranestad, Bernd Sturmfels +1
Every real algebraic variety determines a Voronoi decomposition of its ambient Euclidean space. Each Voronoi cell is a convex semialgebraic set in the normal space of the variety a…
Rational Quartic Spectrahedra
Martin Helsø, Kristian Ranestad
Rational quartic spectrahedra in 3-space are semialgebraic convex subsets in of semidefinite, real symmetric -matrices, whose boundary admits a rationa…
Algebraic Identifiability of Gaussian Mixtures
Carlos Améndola, Kristian Ranestad, Bernd Sturmfels
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 defectiv…
Hyperkähler fourfolds and Kummer surfaces
Atanas Iliev, Grzegorz Kapustka, Michał Kapustka +1
We show that a Hilbert scheme of conics on a Fano fourfold double cover of ramified along a divisor of bidegree admits a -fib…
Varieties of apolar subschemes of toric surfaces
Matteo Gallet, Kristian Ranestad, Nelly Villamizar
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…
EPW Cubes
Atanas Iliev, Grzegorz Kapustka, Michal Kapustka +1
We construct a new 20-dimensional family of projective 6-dimensional irreducible holomorphic symplectic manifolds. The elements of this family are deformation equivalent with the H…
Cremona linearizations of some classical varieties
Ciro Ciliberto, Maria Angelica Cueto, Massimiliano Mella +2
In this paper we present an effective method for linearizing rational varieties of codimension at least two under Cremona transformations, starting from a given parametrization. Us…
Variety of power sums and divisors in the moduli space of cubic fourfolds
Kristian Ranestad, Claire Voisin
We show that a cubic fourfold F that is apolar to a Veronese surface has the property that its variety of power sums VSP(F,10) is singular along a K3 surface of genus 20. We prove…
On the cactus rank of cubics forms
Alessandra Bernardi, Kristian Ranestad
We prove that the smallest degree of an apolar 0-dimensional scheme of a general cubic form in variables is at most , when , and therefore smaller than the ran…
Algebraic boundaries of Hilbert's SOS cones
Grigoriy Blekherman, Jonathan Hauenstein, John Christian Ottem +2
We study the geometry underlying the difference between non-negative polynomials and sums of squares. The hypersurfaces that discriminate these two cones for ternary sextics and qu…
On the rank of a symmetric form
Kristian Ranestad, Frank-Olaf Schreyer
We give a lower bound for the degree of a finite apolar subscheme of a symmetric form F, in terms of the degrees of the generators of the annihilator ideal of F. In the special cas…
Vector bundles on Fano varieties of genus ten
Michal Kapustka, Kristian Ranestad
In this note we describe a unique linear embedding of a prime Fano 4-fold F of genus 10 into the Grassmannian G(3,6). We use this to construct some moduli spaces of bundles on line…
The Convex Hull of a Variety
Kristian Ranestad, Bernd Sturmfels
We present a characterization, in terms of projective biduality, for the hypersurfaces appearing in the boundary of the convex hull of a compact real algebraic variety.
On the convex hull of a space curve
Kristian Ranestad, Bernd Sturmfels
The boundary of the convex hull of a compact algebraic curve in real 3-space defines a real algebraic surface. For general curves, that boundary surface is reducible, consisting of…
Linear precision for toric surface patches
Hans-Christian Graf von Bothmer, Kristian Ranestad, Frank Sottile
We classify the homogeneous polynomials in three variables whose toric polar linear system defines a Cremona transformation. This classification also includes, as a proper subset,…
A general formula for the algebraic degree in semidefinite programming
Hans-Christian Graf von Bothmer, Kristian Ranestad
In this note, we use a natural desingularization of the conormal variety of the variety of n x n symmetric matrices of rank at most r to find a general formula for the algebraic de…
Classification of rational surfaces of degree 11 and sectional genus 11 in P^4
Hans-Christian Graf v. Bothmer, Kristian Ranestad
We use the BGG-correspondence to show that there are at most three possible Hilbert functions for smooth rational surfaces of degree 11 and sectional genus 11. Surfaces with one of…