Alexander Esterov

activity

20162024

collaborators

4 papers

math.AG2024

Engineered complete intersections: slightly degenerate Bernstein--Kouchnirenko--Khovanskii

Alexander Esterov

Geometry of sparse systems of polynomial equations (i.e. the ones with prescribed monomials and generic coefficients) is well studied in terms of their Newton polytopes. The result…

math.AG2024

Schön complete intersections

Alexander Esterov

A complete intersection $f_{1} = \dots = f_{k} = 0$ is schön, if $f_{1} = \dots = f_{j} = 0$ defines a schön subvariety of an algebraic torus for every $j ⩽ k$ . This class includes nondegener…

math.AG2023

Sparse curve singularities, singular loci of resultants, and Vandermonde matrices

Alexander Esterov, Evgeny Statnik, Arina Voorhaar

We compute the $δ$ -invariant of a curve singularity parameterized by generic sparse polynomials. We apply this to describe topological types of generic singularities of sparse resu…

math.AG2016

Signs of the Leading Coefficients of the Resultant

Arina Arkhipova, Alexander Esterov

We construct a certain $\F_2$-valued analogue of the mixed volume of lattice polytopes. This 2-mixed volume cannot be defined as a polarization of any kind of an additive measure,…