57 citations · 275 across the 73 of their papers we have counts for
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Return of the plane evolute
Ragni Piene, Cordian Riener, Boris Shapiro
Below we consider the evolutes of plane real-algebraic curves and discuss some of their complex and real-algebraic properties. In particular, for a given degree , we provid…
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…
On existence of quasi-Strebel structures for meromorphic k-differentials
Boris Shapiro, Guillaume Tahar
In this paper, motivated by the classical notion of a Strebel quadratic differential on a compact Riemann surfaces without boundary we introduce the notion of a quasi-Strebel struc…
On the number of intersection points of the contour of an amoeba with a line
Lionel Lang, Boris Shapiro, Eugenii Shustin
In this note, we investigate the maximal number of intersection points of a line with the contour of hypersurface amoebas in . We define the latter number to be the $…
Moment Varieties of Measures on Polytopes
Kathlén Kohn, Boris Shapiro, Bernd Sturmfels
The uniform probability measure on a convex polytope induces piecewise polynomial densities on its projections. For a fixed combinatorial type of simplicial polytopes, the moments…
On generic and maximal k-ranks of binary forms
Samuel Lundqvist, Alessandro Oneto, Bruce Reznick +1
In what follows, we pose two general conjectures about decompositions of homogeneous polynomials as sums of powers. The first one (suggested by G. Ottaviani) deals with the generic…