38 citations · 272 across the 43 of their papers we have counts for
22 papers · 1 filter
Lefschetz properties for monomial complete intersections
Annet Kyomuhangi, Emanuela Marangone, Claudiu Raicu +1
We give a complete characterization of the weak Lefschetz property (WLP) for monomial complete intersections over a field of positive characteristic. Richard Stanley observed that…
Diagonal F-thresholds for determinants and Pfaffians
Barbara Betti, Claudiu Raicu, Francesco Romeo +1
We compute the diagonal F-thresholds of determinantal hypersurfaces arising from a generic matrix and from a generic symmetric matrix, as well as of the Pfaffian hypersurface arisi…
Powers of binary forms and derived Hermite reciprocity
Claudiu Raicu, Steven V Sam, Jerzy Weyman +1
For , Hilbert found in 1886 a collection of polynomial equations that cut out set-theoretically the variety X parametrizing a-th powers of binary forms of degree b. We d…
Higher resonance schemes and Koszul modules of simplicial complexes
Marian Aprodu, Gavril Farkas, Claudiu Raicu +2
Each connected graded, graded-commutative algebra of finite type over a field of characteristic zero defines a complex of finitely generated, graded modules over a symm…
On some modules supported in the Chow variety
Claudiu Raicu, Steven V Sam, Jerzy Weyman
The study of Chow varieties of decomposable forms lies at the confluence of algebraic geometry, commutative algebra, representation theory and combinatorics. There are many open qu…
An equivariant Hochster's formula for -invariant monomial ideals
Satoshi Murai, Claudiu Raicu
Let be a polynomial ring over a field and let be a monomial ideal preserved by the natural action of the symmetric group $\mathfrak S_…
Regularity of S_n-invariant monomial ideals
Claudiu Raicu
For a polynomial ring S in n variables, we consider the natural action of the symmetric group S_n on S by permuting the variables. For an S_n-invariant monomial ideal I in S and j…
Relations between the 2x2 minors of a generic matrix
Hang Huang, Michael Perlman, Claudia Polini +2
We prove the case t = 2 of a conjecture of Bruns-Conca-Varbaro, describing the minimal relations between the t x t minors of a generic matrix. Interpreting these relations as polyn…
Bi-graded Koszul modules, K3 carpets, and Green's conjecture
Claudiu Raicu, Steven V Sam
We extend the theory of Koszul modules to the bi-graded case, and prove a vanishing theorem that allows us to show that the Canonical Ribbon Conjecture of Bayer and Eisenbud holds…
Computing Schur complexes
Michael K. Brown, Hang Huang, Robert P. Laudone +4
We describe a Macaulay2 package for computing Schur complexes. This package expands on the ChainComplexOperations package by David Eisenbud.
Syzygies of determinantal thickenings and representations of the general linear Lie superalgebra
Claudiu Raicu, Jerzy Weyman
We let S denote the ring of polynomial functions on the space of m x n matrices, and consider the action of the group GL = GL_m x GL_n via row and column operations on the matrix e…
Iterated local cohomology groups and Lyubeznik numbers for determinantal rings
András C. Lőrincz, Claudiu Raicu
We give an explicit recipe for determining iterated local cohomology groups with support in ideals of minors of a generic matrix in characteristic zero, expressing them as direct s…
Homological invariants of determinantal thickenings
Claudiu Raicu
The study of homological invariants such as Tor, Ext and local cohomology modules constitutes an important direction in commutative algebra. Explicit descriptions of these invarian…
Equivariant D-modules on binary cubic forms
András C. Lőrincz, Claudiu Raicu, Jerzy Weyman
We consider the space X = Sym^3(C^2) of binary cubic forms, equipped with the natural action of the group GL_2 of invertible linear transformations of C^2. We describe explicitly t…
On the (non-)vanishing of syzygies of Segre embeddings
Luke Oeding, Claudiu Raicu, Steven V Sam
We analyze the vanishing and non-vanishing behavior of the graded Betti numbers for Segre embeddings of products of projective spaces. We give lower bounds for when each of the row…
Regularity and cohomology of determinantal thickenings
Claudiu Raicu
We consider the ring S=C[x_ij] of polynomial functions on the vector space C^(m x n) of complex m x n matrices. We let GL= GL_m x GL_n and consider its action via row and column op…
Local cohomology with support in ideals of symmetric minors and Pfaffians
Claudiu Raicu, Jerzy Weyman
We compute the local cohomology modules H_Y^(X,O_X) in the case when X is the complex vector space of n x n symmetric, respectively skew-symmetric matrices, and Y is the closure of…
The syzygies of some thickenings of determinantal varieties
Claudiu Raicu, Jerzy Weyman
The vector space of m x n complex matrices (m >= n) admits a natural action of the group GL = GL_m x GL_n via row and column operations. For positive integers a,b, we consider the…
Introduction to uniformity in commutative algebra
Craig Huneke, Claudiu Raicu
These notes are based on three lectures given by the first author as part of an introductory workshop at MSRI for the program in Commutative Algebra, 2012-13. The notes follow the…
Local cohomology with support in ideals of maximal minors and sub-maximal Pfaffians
Claudiu Raicu, Jerzy Weyman, Emily E. Witt
We compute the GL-equivariant description of the local cohomology modules with support in the ideal of maximal minors of a generic matrix, as well as of those with support in the i…
Non-simplicial decompositions of Betti diagrams of complete intersections
Courtney Gibbons, Jack Jeffries, Sarah Mayes +3
We investigate decompositions of Betti diagrams over a polynomial ring within the framework of Boij--Soederberg theory. That is, given a Betti diagram, we decompose it into pure di…
Local cohomology with support in ideals of maximal minors
Emily E. Witt
Suppose that k is a field of characteristic zero, X is an r by s matrix of indeterminates, where r \leq s, and R = k[X] is the polynomial ring over k in the entries of X. We study…