6 citations · 44 across the 16 of their papers we have counts for
9 papers · 1 filter
Combinatorial study of morsifications of real univariate singularities
Arnaud Bodin, Evelia Rosa García Barroso, Patrick Popescu-Pampu +1
We study a broad class of morsifications of germs of univariate real analytic functions. We characterize the combinatorial types of the resulting Morse functions, via planar contac…
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…
A generalization of the space of complete quadrics
Abeer Al Ahmadieh, Mario Kummer, Miruna-Stefana Sorea
To any homogeneous polynomial we naturally associate a variety which maps birationally onto the graph of the gradient map and which agrees with the space…
The structure of the moduli space of toric dynamical systems of a reaction network
Gheorghe Craciun, Jiaxin Jin, Miruna-Stefana Sorea
We consider toric dynamical systems, which are also called complex-balanced mass-action systems. These are remarkably stable polynomial dynamical systems that arise from the analys…
Disguised toric dynamical systems
Laura Brustenga i Moncusí, Gheorghe Craciun, Miruna-Stefana Sorea
We study families of polynomial dynamical systems inspired by biochemical reaction networks. We focus on complex balanced mass-action systems, which have also been called toric. Th…
Permutations encoding the local shape of level curves of real polynomials via generic projections
Miruna-Stefana Sorea
The non-convexity of a smooth and compact connected component of a real algebraic plane curve can be measured by a combinatorial object called the Poincare-Reeb tree associated to…
On the eigenpoints of cubic surfaces
Türkü Özlüm Celik, Francesco Galuppi, Avinash Kulkarni +1
We show that the eigenschemes of symmetric tensors are parametrized by a linear subvariety of the Grassmannian . We also…
Measuring the local non-convexity of real algebraic curves
Miruna-Stefana Sorea
The goal of this paper is to measure the non-convexity of compact and smooth connected components of real algebraic plane curves. We study these curves first in a general setting a…
Constructing Separable Arnold Snakes of Morse Polynomials
Miruna-Stefana Sorea
We give a new and constructive proof of the existence of a special class of univariate polynomials whose graphs have preassigned shapes. By definition, all the critical points of a…