15 citations · 47 across the 26 of their papers we have counts for
24 papers · 1 filter
Local dimension testing via quadratic obstructions
Taylor Brysiewicz, Rainer Sinn
We give an algorithm, based on second-order necessary conditions, to test whether a point is isolated on an algebraic set. Using this subroutine, we develop an algorithm that bound…
Pythagoras Numbers for Ternary Forms
Grigoriy Blekherman, Alex Dunbar, Rainer Sinn
We study the Pythagoras numbers of real ternary forms, defined for each degree as the minimal number such that every degree ternary form which is a sum of…
Nonnegativity certificates on real algebraic surfaces
Grigoriy Blekherman, Rainer Sinn, Gregory G. Smith +1
We introduce tools for transferring nonnegativity certificates for global sections between line bundles on real algebraic surfaces. As applications, we improve Hilbert's degree bou…
Nonnegative Polynomials and Moment Problems on Algebraic Curves
Lorenzo Baldi, Grigoriy Blekherman, Rainer Sinn
The cone of nonnegative polynomials is of fundamental importance in real algebraic geometry, but its facial structure is understood in very few cases. We initiate a systematic stud…
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…
Weak and Strong Extremal Biquadratics
Grigoriy Blekherman, Bogdan Raiţă, Isabelle Shankar +1
We study quasiconvex quadratic forms on matrices which correspond to nonnegative biquadratic forms in variables. We disprove a conjecture stated by Harutyunyan…