4 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…
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…
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…
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…