8 citations · 17 across the 6 of their papers we have counts for
6 papers
Sparse curve singularities, singular loci of resultants, and Vandermonde matrices
Alexander Esterov, Evgeny Statnik, Arina Voorhaar
We compute the -invariant of a curve singularity parameterized by generic sparse polynomials. We apply this to describe topological types of generic singularities of sparse resu…
On vanishing theorems for local systems associated to Laurent polynomials
Alexander Esterov, Kiyoshi Takeuchi
We prove some vanishing theorems for the cohomology groups of local systems associated to Laurent polynomials. In particular, we extend one of the results of Gelfand-Kapranov-Zelev…
On the monodromy conjecture for non-degenerate hypersurfaces
Alexander Esterov, Ann Lemahieu, Kiyoshi Takeuchi
The monodromy conjecture is an umbrella term for several conjectured relationships between poles of zeta functions, monodromy eigenvalues and roots of Bernstein-Sato polynomials in…
Motivic Milnor fibers over complete intersection varieties and their virtual Betti numbers
Alexander Esterov, Kiyoshi Takeuchi
We study the Jordan normal forms of the local and global monodromies over complete intersection subvarieties of by using the theory of motivic Milnor fibers. The results will…
Determinantal singularities and Newton polyhedra
Alexander Esterov
There are two well known tasks, related to Newton polyhedra: to study invariants of singularities in terms of their Newton polyhedra, and to describe Newton polyhedra of resultants…
Newton polyhedra of discriminants of projections
Alexander Esterov
For a system of polynomial equations, whose coefficients depend on parameters, the Newton polyhedron of its discriminant is computed in terms of the Newton polyhedra of the coeffic…