23 citations · 32 across the 13 of their papers we have counts for
19 papers
The monodromy conjecture for high order poles, and norms of residue antiderivatives
Alexander Esterov
We prove the strong local monodromy conjecture for poles of order at least of the naive motivic zeta-function for a complex polynomial of variables. Moreover, for every s…
Whitney fold and cusp for algebraic surfaces, and singularities of discriminants
Alexander Esterov, Lev Vladimirov, Aliaksandr Yuran
We describe transversal singularity types of the singular locus of the -discriminant for , and deduce a Whitney type theorem for a coordinate projection of a…
Basecondary polytopes
Alexander Esterov, Arina Voorhaar
Many (if not most) of convex polytopes, important for combinatorial and algebraic geometry, are closely related to secondary polytopes of point configurations, or base polytopes of…
Gauss--Bonnet for CSM classes of very affine manifolds, and tropical isotopies
Alexander Esterov
The CSM class of a very affine manifold is represented by the rank drop locus of a general tuple of torus invariant 1-forms on it. This equality holds in the homology of any to…
Bernstein-Kouchnirenko-Khovanskii with a symmetry
Alexander Esterov, Lionel Lang
A generic polynomial f(x,y,z) with a prescribed Newton polytope defines a symmetric spatial curve f(x,y,z)=f(y,x,z)=0. We study its geometry: the number, degree and genus of its ir…
Permuting the roots of univariate polynomials whose coefficients depend on parameters
Alexander Esterov, Lionel Lang
We address two interrelated problems concerning the permutation of roots of univariate polynomials whose coefficients depend on parameters. First, we compute the Galois group of po…
Braid monodromy of univariate fewnomials
Alexander Esterov, Lionel Lang
Let be the space of non-singular, univariate polynomials of degree . The Viète map $\mathscr{V} : \mathcal{C}_d \rightarrow Sym_d(\mathbb…
Sparse polynomial equations and other enumerative problems whose Galois groups are wreath products
Alexander Esterov, Lionel Lang
We introduce a new technique to prove connectivity of subsets of covering spaces (so called inductive connectivity), and apply it to Galois theory of problems of enumerative geomet…
The ring of local tropical fans and tropical nearby monodromy eigenvalues
Alexander Esterov
We extend the tropical intersection theory to tropicalizations of germs of analytic sets. In particular, we construct a (not entirely obvious) local version of the ring of tropical…
Galois theory for general systems of polynomial equations
Alexander Esterov
We prove that the monodromy group of a reduced irreducible square system of general polynomial equations equals the symmetric group. This is a natural first step towards the Galois…
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,…
Multivariate Abel-Ruffini
Alexander Esterov, Gleb Gusev
We classify general square systems of polynomial equations solvable in radicals. Expectedly, they are almost in a 1-to-1 correspondence with tuples of lattice polytopes of mixed vo…
Monodromies at infinity of confluent A-hypergeometric functions
Kana Ando, Alexander Esterov, Kiyoshi Takeuchi
We study the monodromies at infinity of confluent A-hypergeometric functions introduced by Adolphson. In particular, we extend the result of the third author for non-confluent A-hy…
Characteristic classes of affine varieties and Plucker formulas for affine morphisms
Alexander Esterov
An enumerative problem on a variety is usually solved by reduction to intersection theory in the cohomology of a compactification of . However, if the problem is invariant u…
Systems of equations with a single solution
Alexander Esterov, Gleb Gusev
We classify general systems of polynomial equations with a single solution, or, equivalently, collections of lattice polytopes of minimal positive mixed volume. As a byproduct, thi…
Multiplicities of degenerations of matrices and mixed volumes of Cayley polyhedra
Alexander Esterov
Using a certain Pick-type formula for the mixed volume of Cayley polyhedra, we compute the multiplicity of the isolated common zero of the maximal minors for a matrix of generic ho…
Discriminant of system of equations
Alexander Esterov
What polynomial in the coefficients of a system of algebraic equations should be called its discriminant? We prove a package of facts that provide a possible answer. Let us call a…
Confluent A-hypergeometric functions and rapid decay homology cycles
Alexander Esterov, Kiyoshi Takeuchi
We study confluent A-hypergeometric functions introduced by Adolphson. In particular, we give their integral representations by using rapid decay homology cycles of Hien and obtain…
Tropical varieties with polynomial weights and corner loci of piecewise polynomials
Alexander Esterov
We find a relation between mixed volumes of several polytopes and the convex hull of their union, deducing it from the following fact: the mixed volume of a collection of polytopes…