5 papers
A note on bounded ratios
Lorenzo Baldi, Mario Kummer
We prove that the set of bounded ratios $\BR(X)$ on a semialgebraic set is the convex cone of linear forms that are nonnegative on the tropicalization $\trop(X)…
Stubborn Polynomials
Lorenzo Baldi, Grigoriy Blekherman, Khazhgali Kozhasov +3
The relationship between nonnegative polynomials and sums of squares is a classical topic in real algebraic geometry. We study \emph{stubborn polynomials} on a real variety …
Toric extensions of Pólya's theorem
Lorenzo Baldi, Rainer Sinn, Máté L. Telek +1
The classical version of Pólya's theorem provides a simple method for certifying that a homogeneous polynomial of degree d is strictly copositive, that is, it takes only positive v…
Totally real divisors on curves
Lorenzo Baldi, Mario Kummer, Daniel Plaumann
Since the works of Krasnov and Scheiderer, there has been an interest in studying effective totally real divisors on a curve X defined over a real closed field, i.e., effective div…
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…