Related papers: Hodge ideals for Q-divisors, V-filtration, and min…

For $i : Z \to X$ a closed immersion of smooth varieties, we study how the $V$-filtration along $Z$ and the Hodge filtration on a mixed Hodge module $M$ on $X$ interact with each other. We also give a formula for the functors $i^*$, $i^!$…

For a reduced monomial ideal B in R=k[X_1,...,X_n], we write H^i_B(R) as the union of {Ext^i(R/B^[d],R)}_d, where {B^[d]}_d are the "Frobenius powers of B". We describe H^i_B(R)_p, for every p in Z^n, in the spirit of the Stanley-Reisner…

We show that the Hodge and pole order filtrations are globally different for sufficiently general singular projective hypersurfaces in case the degree is 3 or 4 assuming the dimension of the projective space is at least 5 or 3 respectively.…

Some affirmative answers are given to Huneke's problems. The calculation of local cohomology modules with respect to an arbitrary pair of ideals $I,J$ can be reduced to calculation of local cohomology modules with respect to a pair of…

Several relations and bounds for the dimension of principal ideals in group algebras are determined by analyzing minimal polynomials of regular representations. These results are used in the two last sections. First, in the context of…

In this paper, we study the Chevalley property of Cayley-Hamilton Hopf algebras in the sense of De Concini-Procesi-Reshetikhin-Rosso using discriminant ideals. For any affine Cayley-Hamilton Hopf algebra $(H,C,\text{tr})$ whose identity…

Discriminant ideals of noncommutative algebras $A$, which are module finite over a central sublagebra $C$, are key invariants that carry important information about $A$, such as the sum of the squares of the dimensions of its irreducible…

We define {\bf primitive derivations} for Coxeter arrangements which may not be irreducible. Using those derivations, we introduce the {\bf primitive filtrations} of the module of invariant logarithmic differential forms for an arbitrary…

The notions Hodge-Newton decomposition and Hodge-Newton filtration for F-crystals are due to Katz and generalize Messing's result on the existence of the local-\'etale filtration for p-divisible groups. Recently, some of Katz's classical…

In this work we describe a minimal log-resolution of an ideal in a smooth complex surface from the minimal log-resolution of its generators.

We consider a filtration on the cohomology of the structure sheaf indexed by (not necessarily reduced) divisors ``at infinity''. We show that the filtered pieces have transfers morphisms, fpqc descent, and are so called cube invariant. In…

We give an explicit formula to express the cohomological pullback functors of Hodge modules under closed immersions of smooth varieties using Verdier specializations and $V$-filtrations of Kashiwara and Malgrange. This was locally obtained…

Our starting point is a basic problem in Hermite interpolation theory, namely determining the least degree of a homogeneous polynomial that vanishes to some specified order at every point of a given finite set. We solve this problem if the…

We extend previous work to the case of $\mathbb{Q}$-divisors. Namely, for certain parametrically prime holomorphic functions $f$ and $\alpha \geq 0$, we obtain an explicit expression for the Hodge filtration on…

This first part of the paper describes the support of top graded local cohomology modules. As a corrolary one obtains a simple criteria for the vanishing of these modules and also the fact that they have finitely many minimal primes. The…

For a projective variety V in P^n over a field of characteristic zero, with homogeneous ideal I in A = k[x0,x1,...,xn], we consider the local cohomology modules H^i_I(A). These have a structure of holonomic D-module over A, and we…

Let g be a complex reductive Lie algebra and U(g) the universal enveloping algebra of g. Associated to a faithful irreducible finite dimensional representation of g, a square matrix F with entries in U(g) naturally arises and if we consider…

We consider ideals arising in the context of conditional independence models that generalize the class of ideals considered by Fink [7] in a way distinct from the generalizations of Herzog-Hibi-Hreinsdottir-Kahle-Rauh [13] and Ay-Rauh [1].…

We show that the minimal resolution of the quotient of the polynomial algebra over a field by a cointerval edge ideal can be given the structure of a DG-algebra.

Let $k$ be an infinite field and $I\subset k [x_1, \ldots ,x_n]$ be an ideal such that dim $V(I)=q$. Denote by $(f_1, \ldots, f_s)$ a set of generators of $I$. One can see that in the set $I\cap k [x_{1},...,x_{q+1}]$ there exist non-zero…