6 papers · 1 filter
Degenerating Discriminants
Viktoriia Borovik, Clara Briand
We study the behavior of projective dual varieties and discriminants under flat degenerations. For Gröbner degenerations, we show that the conormal variety admits a Gröbner degener…
Numerical Algebraic Geometry for Energy Computations on Tensor Train Varieties
Viktoriia Borovik, Hannah Friedman, Serkan Hoşten +1
We study energy minimization problems in quantum chemistry through the lens of computational algebraic geometry. We focus on minimizing the Rayleigh quotient of a Hamiltonian over…
On the construction of a counterexample to Strassen's rank additivity conjecture
Viktoriia Borovik, Cosimo Flavi, Paweł Pielasa +2
The rank additivity conjecture, first formulated by Volker Strassen in 1973, states that the rank of the direct sum of two independent tensors is equal to the sum of their individu…
The SagbiHomotopy.jl package for solving polynomial systems
Barbara Betti, Viktoriia Borovik
We present the Julia package SagbiHomotopy.jl for solving systems of polynomial equations using numerical homotopy continuation. The package introduces an optimal choice of a start…
Proudfoot-Speyer degenerations of scattering equations
Barbara Betti, Viktoriia Borovik, Simon Telen
We study scattering equations of hyperplane arrangements from the perspective of combinatorial commutative algebra and numerical algebraic geometry. We formulate the problem as lin…
Additive actions on projective hypersurfaces with a finite number of orbits
Viktoriia Borovik, Alexander Chernov, Anton Shafarevich
An induced additive action on a projective variety is a regular action of the group on with an open orbit, which can be extended to…