4 citations · 16 across the 11 of their papers we have counts for
14 papers
Bernstein's inequality and holonomicity for certain singular rings
Josep Àlvarez Montaner, Daniel J. Hernández, Jack Jeffries +3
In this manuscript we prove the Bernstein inequality and develop the theory of holonomic D-modules for rings of invariants of finite groups in characteristic zero, and for strongly…
Bernstein-Sato functional equations, -filtrations, and multiplier ideals of direct summands
Josep Àlvarez Montaner, Daniel J. Hernández, Jack Jeffries +3
This paper investigates the existence and properties of a Bernstein-Sato functional equation in nonregular settings. In particular, we construct -modules in which such formal eq…
The FrobeniusThresholds package for Macaulay2
Daniel J. Hernández, Karl Schwede, Pedro Teixeira +1
This article describes the \emph{Macaulay2} package \emph{FrobeniusThresholds}, designed to estimate and calculate -pure thresholds, more general -thresholds, and related num…
The TestIdeals package for Macaulay2
Alberto F. Boix, Daniel J. Hernández, Zhibek Kadyrsizova +7
This note describes a \emph{Macaulay2} package for computations in prime characteristic commutative algebra. This includes Frobenius powers and roots, -linear and -l…
Frobenius powers of some monomial ideals
Daniel J. Hernández, Pedro Teixeira, Emily E. Witt
In this paper, we characterize the (generalized) Frobenius powers and critical exponents of two classes of monomial ideals of a polynomial ring in positive characteristic: powers o…
Frobenius powers
Daniel J. Hernández, Pedro Teixeira, Emily E. Witt
This article extends the notion of a Frobenius power of an ideal in prime characteristic to allow arbitrary nonnegative real exponents. These generalized Frobenius powers are close…
Addendum to: Dacorogna-Moser theorem on the Jacobian determinant equation with control of support
Pedro Teixeira
In Dacorogna-Moser theorem on the pullback equation between two prescribed volume forms (with the same total volume), control of support of the solutions can be obtaine…
On the conservative pasting lemma
Pedro Teixeira
Several perturbation tools are established in the volume preserving setting allowing for the pasting, extension, localized smoothing and local linearization of vector fields. The p…
Dacorogna-Moser theorem on the Jacobian determinant equation with control of support
Pedro Teixeira
The original proof of Dacorogna-Moser theorem on the prescribed Jacobian PDE, , can be modified in order to obtain control of support of the solutions from t…
F-threshold functions: syzygy gap fractals and the two-variable homogeneous case
Daniel J. Hernández, Pedro Teixeira
In this article we study F-pure thresholds (and, more generally, F-thresholds) of homogeneous polynomials in two variables over a field of characteristic p>0. Passing to a field ex…
Topological detection of Lyapunov instability
Pedro Teixeira
Given an arbitrary continuous flow on a manifold M, let CMin be the set of its compact minimal sets, endowed with the Hausdorff metric, and S the subset of those that are Lyapunov…
Flows near Compact Invariant Sets - Part I
Pedro Teixeira
In this paper it is proved that near a compact, invariant, proper subset of a continuous flow on a compact, connected metric space, at least one, out of twenty eight relevant dynam…
Syzygy gap fractals--I. Some structural results and an upper bound
Pedro Teixeira
k is a field of characteristic p>0, and l_1,...,l_n are linear forms in k[x,y]. Intending applications to Hilbert--Kunz theory, to each triple C=(F,G,H) of nonzero homogeneous elem…
p-Fractals and power series--II. Some applications to Hilbert-Kunz theory
Paul Monsky, Pedro Teixeira
We use the results of our paper "p-Fractals and power series--I" (Journal of Algebra 280, 2004, pp. 505--536) to prove the rationality of the Hilbert-Kunz series of a large family…