38 citations · 272 across the 43 of their papers we have counts for
51 papers
Suciu's Conjecture on hyperplane arrangements
Marian Aprodu, Gavril Farkas, Claudiu Raicu +1
We prove that the resonance of any hyperplane arrangement is separable. Using the main result from arXiv:2512.10160 this proves Suciu's conjecture on the fundamental group of every…
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…
Cohomology characters on the incidence correspondence
Annet Kyomuhangi, Emanuela Marangone, Claudiu Raicu +1
We investigate the cohomology of line bundles on the incidence correspondence, the partial flag variety parametrizing pairs consisting of a point in projective space and a hyperpla…
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…
The effective Chen ranks conjecture
Marian Aprodu, Gavril Farkas, Claudiu Raicu +1
Koszul modules and their associated resonance schemes are objects appearing in a variety of contexts in algebraic geometry, topology, and combinatorics. We present a proof of an ef…
Stable sheaf cohomology and Koszul--Ringel duality
Claudiu Raicu, Keller VandeBogert
We identify a close relationship between stable sheaf cohomology for polynomial functors applied to the cotangent bundle on projective space, and Koszul--Ringel duality on the cate…
Computing the cohomology of line bundles on the incidence correspondence and related invariants
Annet Kyomuhangi, Emanuela Marangone, Claudiu Raicu +1
We describe the package "IncidenceCorrespondenceCohomology" for the computer algebra system Macaulay2. The main feature concerns the computation of characters and dimensions for th…
Cohomology on the incidence correspondence and related questions
Annet Kyomuhangi, Emanuela Marangone, Claudiu Raicu +1
We study a variety of questions centered around the computation of cohomology of line bundles on the incidence correspondence (the partial flag variety parametrizing pairs consisti…
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…
Some questions arising from the study of cohomology on flag varieties
Zhao Gao, Claudiu Raicu, Keller VandeBogert
A fundamental problem at the confluence of algebraic geometry and representation theory is to describe the cohomology of line bundles on flag varieties over a field of characterist…
Stable sheaf cohomology on flag varieties
Claudiu Raicu, Keller VandeBogert
We prove an effective stabilization result for the sheaf cohomology groups of line bundles on flag varieties parametrizing complete flags in k^n, as well as for the sheaf cohomolog…
Reduced resonance schemes and Chen ranks
Marian Aprodu, Gavril Farkas, Claudiu Raicu +1
The resonance varieties are cohomological invariants that are studied in a variety of topological, combinatorial, and geometric contexts. We discuss their scheme structure in a gen…
Cohomology of line bundles on the incidence correspondence
Zhao Gao, Claudiu Raicu
For a finite dimensional vector space V of dimension n, we consider the incidence correspondence (or partial flag variety) X in P(V) x P(V*), parametrizing pairs consisting of a po…
Koszul modules with vanishing resonance in algebraic geometry
Marian Aprodu, Gavril Farkas, Claudiu Raicu +1
We discuss various applications of a uniform vanishing result for the graded components of the finite length Koszul module associated to a subspace in the second wedge product of a…
Borel-Moore homology of determinantal varieties
András C. Lőrincz, Claudiu Raicu
We compute the rational Borel-Moore homology groups for affine determinantal varieties in the spaces of general, symmetric, and skew-symmetric matrices, solving a problem suggested…
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…
Hermite reciprocity and Schwarzenberger bundles
Claudiu Raicu, Steven V Sam
Hermite reciprocity refers to a series of natural isomorphisms involving compositions of symmetric, exterior, and divided powers of the standard -representation. We survey se…
Euler obstructions for the Lagrangian Grassmannian
Paul LeVan, Claudiu Raicu
We prove a case of a positivity conjecture of Mihalcea-Singh, concerned with the local Euler obstructions associated to the Schubert stratification of the Lagrangian Grassmannian L…
Local Euler obstructions for determinantal varieties
András C. Lőrincz, Claudiu Raicu
The goal of this note is to explain a derivation of the formulas for the local Euler obstructions of determinantal varieties of general, symmetric and skew-symmetric matrices, by s…
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_…
Hodge ideals for the determinant hypersurface
Michael Perlman, Claudiu Raicu
We determine explicitly the Hodge ideals for the determinant hypersurface as an intersection of symbolic powers of determinantal ideals. We prove our results by studying the Hodge…
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…
Feasibility criteria for high-multiplicity partitioning problems
Claudiu Raicu
For fixed weights w_1,...,w_n, and for d>0, we let B denote a collection of d*n balls, with d balls of weight w_i for each i=1,...,n. We consider the problem of assigning the balls…