53 citations · 273 across the 39 of their papers we have counts for
44 papers
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…
Algebraic Degrees of Generalized Nash Equilibrium Problems
Jiawang Nie, Kristian Ranestad, Xindong Tang
This paper studies the algebraic degree of generalized Nash equilibrium problems (GNEPs) given by polynomials. Their generalized Nash equilibria (GNEs), as well as their KKT or Fri…
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…
Quaternary quartic forms and Gorenstein rings
Gregorz Kapustka, Michał Kapustka, Kristian Ranestad +3
A quaternary quartic form, a quartic form in four variables, is the dual socle generator of an Artinian Gorenstein ring of codimension and regularity 4. We present a classification…