Regularity, singularities and $h$-vector of graded algebras

Singularities in algebraic geometry (14B05) Graded rings (13A02) Local cohomology and commutative rings (13D45) Local cohomology and algebraic geometry (14B15) Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35)

Cites Work

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Regularity of canonical and deficiency modules for monomial ideals
On the $h$-vector of a simplicial complex with Serre's condition
Eulerian graded $\mathcal{D}$-modules
Linear free resolutions and minimal multiplicity
$H$-vectors of simplicial complexes with Serre's conditions
The canonical sheaf of Du Bois singularities
Dualisierende Komplexe in der lokalen Algebra und Buchsbaum-Ringe
The purity of the Frobenius and local cohomology
Laurent coefficients and Ext of finite graded modules
Etale cohomological dimension and the topology of algebraic varieties
Mather discrepancy and the arc spaces
Alexander duality for Stanley-Reisner rings and squarefree $\mathbb{N}^n$-graded modules
$F$-injectivity and Buchsbaum singularities
Jacobian discrepancies and rational singularities
Singularities with respect to Mather-Jacobian discrepancies
A vanishing theorem for log canonical pairs
Hodge theory meets the minimal model program: a survey of log canonical and Du Bois singularities
Small schemes and varieties of minimal degree
A Simple Characterization of Du Bois Singularities
Complete Intersections and Connectedness
A Remark Concerning Multiplicities
Vanishing Theorems, A Theorem of Severi, and the Equations Defining Projective Varieties
Mather–Jacobian singularities under generic linkage
The Geometry of Syzygies
Liaison and Castelnuovo-Mumford regularity
Cohomologically Full Rings
Deformations of log canonical and $F$-pure singularities
Local cohomology of Du Bois singularities and applications to families
Stabilization of the cohomology of thickenings
Gröbner deformations and F‐singularities

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Regularity, singularities and \(h\)-vector of graded algebras