4 Citations
A Note on Bernstein-Sato Varieties for Tame Divisors and Arrangements
- Mathematics
- 2020
For strongly Euler-homogeneous, Saito-holonomic, and tame analytic germs we consider general types of multivariate Bernstein-Sato ideals associated to arbitrary factorizations of our germ. We show…
Estimates for zero loci of Bernstein-Sato ideals
- Mathematics
- 2021
We give estimates for the zero loci of Bernstein-Sato ideals. An upper bound is proved as a multivariate generalisation of the upper bound by Lichtin for the roots of Bernstein-Sato polynomials. The…
Monodromy conjecture for log generic polynomials
- MathematicsMathematische Zeitschrift
- 2022
A log generic hypersurface in $\mathbb{P}^n$ with respect to a birational modification of $\mathbb{P}^n$ is by definition the image of a generic element of a high power of an ample linear series on…
Maximum Likelihood Estimation from a Tropical and a Bernstein--Sato Perspective
- Mathematics
- 2021
In this article, we investigate Maximum Likelihood Estimation with tools from Tropical Geometry and Bernstein--Sato theory. We investigate the critical points of very affine varieties and study their…
References
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Bernstein-Sato ideals and local systems
- Mathematics
- 2012
The topology of smooth quasi-projective complex varieties is very restrictive. One aspect of this statement is the fact that natural strata of local systems, called cohomology support loci, have a…
Bernstein–Sato polynomials of hyperplane arrangements
- Mathematics
- 2006
We show that the Bernstein–Sato polynomial (that is, the b-function) of a hyperplane arrangement with a reduced equation is calculable by combining a generalization of Malgrange’s formula with the…
The Monodromy Conjecture for hyperplane arrangements
- Mathematics
- 2009
The Monodromy Conjecture asserts that if c is a pole of the local topological zeta function of a hypersurface, then exp(2πic) is an eigenvalue of the monodromy on the cohomology of the Milnor fiber.…
Multiplier ideals, V-filtration, and spectrum
- Mathematics
- 2003
For an effective divisor on a smooth algebraic variety or a complex manifold, we show that the associated multiplier ideals coincide essentially with the filtration induced by the filtration V…
Zero loci of Bernstein–Sato ideals
- Mathematics
- 2019
We prove a conjecture of the first author relating the Bernstein-Sato ideal of a finite collection of multivariate polynomials with cohomology support loci of rank one complex local systems. This…
Jumping coefficients of multiplier ideals
- Mathematics
- 2003
We study in this paper some local invariants attached via multiplier ideals to an effective divisor or ideal sheaf on a smooth complex variety. First considered (at least implicitly) by Libgober and…
Local systems over complements of hyperplanes and the Kac-Kazhdan conditions for singular vectors
- Mathematics
- 1994
Zero loci of Bernstein-Sato ideals-II
- Mathematics
- 2021
We have recently proved a precise relation between Bernstein-Sato ideals of collections of polynomials and monodromy of generalized nearby cycles. In this article we extend this result to other…
The Gauss map and a noncompact Riemann-Roch formula for constructible sheaves on semiabelian varieties
- Mathematics
- 1999
For an irreducible subvariety Z in an algebraic group G we define a nonnegative integer gdeg(Z) as the degree, in a certain sense, of the Gauss map of Z. It can be regarded as a substitution for the…