Open problems in deformations of Artinian algebras, Hilbert schemes and around

DOI10.1090/conm/805/16122MaRDI QIDQ6630003

Publication date: 30 October 2024

deformations Artin algebras tensors Hilbert scheme of points zero-dimensional schemes algebraic geometry of complexity theory quot scheme of points

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Parametrization (Chow and Hilbert schemes) (14C05) Deformations and infinitesimal methods in commutative ring theory (13D10)

Cites Work

Irreducibility of the Hilbert schemes of points on surfaces with Kleinian singularities
New elementary components of the Gorenstein locus of the Hilbert scheme of points
Approximating commuting operators
The variety of pairs of commuting nilpotent matrices is irreducible
Hilbert schemes, separated variables, and \(D\)-branes
Making waves
Concise tensors of minimal border rank
A sign that used to annoy me, and still does
Small elementary components of Hilbert schemes of points
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On the universal family of Hilbert schemes of points on a surface
The variety of polar simplices
On varieties of commuting triples. III.
The Hilbert scheme of a plane curve singularity and the HOMFLY polynomial of its link
On the homology of the Hilbert scheme of points in the plane
Rational components of Hilbert schemes
Deformation classes of graded modules and maximal Betti numbers
Irreducibility of the Gorenstein loci of Hilbert schemes via ray families
Fifteen characterizations of rational double points and simple critical points
Variétés kähleriennes dont la première classe de Chern est nulle
Correction to: ``The complexity of factors of multivariate polynomials
On some Gorenstein loci in \(\mathcal Hilb_6(\mathbb P^4_k)\)
Matrix multiplication via arithmetic progressions
The moduli space of commutative algebras of finite rank
Donaldson-Thomas type invariants via microlocal geometry
Symmetric obstruction theories and Hilbert schemes of points on threefolds
Curve counting via stable pairs in the derived category
Hilbert schemes of 8 points
On the order of approximation in approximative triadic decompositions of tensors
Generic finite schemes and Hochschild cocycles
Description de Hilb sup(n) C{X,Y}
Deformation of schemes defined by vanishing of Pfaffians
Dimension of the punctual Hilbert scheme
Betti numbers of compressed level algebras
Vanishing theorems and character formulas for the Hilbert scheme of points in the plane
Irreducibility of the punctual quotient scheme of a surface
Four counterexamples in combinatorial algebraic geometry
Homology of Hilbert schemes of points on a locally planar curve
Finite schemes and secant varieties over arbitrary characteristic
The Hilbert scheme of 11 points in \(\mathbb{A}^3\) is irreducible
The complexity of factors of multivariate polynomials
VSPs of cubic fourfolds and the Gorenstein locus of the Hilbert scheme of 14 points on \(\mathbb{A}^6\)
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Components and singularities of Quot schemes and varieties of commuting matrices
Bounds on complexity of matrix multiplication away from Coppersmith-Winograd tensors
Irreducibility and singularities of some nested Hilbert schemes
Towards a geometric approach to Strassen's asymptotic rank conjecture
Smooth and irreducible multigraded Hilbert schemes
Versal deformations and local Hilbert schemes
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Abelian tensors
Some elementary components of the Hilbert scheme of points
Constructions of \(k\)-regular maps using finite local schemes
On the Gorenstein locus of the punctual Hilbert scheme of degree 11
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Non-connected toric Hilbert schemes
Connectedness of Hilbert scheme
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DEGENERATION OF SEMISIMPLE ALGEBRAS
Poincaré Series and Deformations of Gorenstein Local Algebras
Isomorphism classes of short Gorenstein local rings via Macaulay’s inverse system
Determinantal equations for secant varieties and the Eisenbud-Koh-Stillman conjecture
Gorenstein modules of finite length
Pairs of Matrices With Property L. II
Géométrie des schémas de Hilbert ponctuels
Compressed Algebras: Artin Algebras Having Given Socle Degrees and Maximal Length
Deformations of Algebraic Schemes
Powers of tensors and fast matrix multiplication
Deformation Theory
Multiple Points, Chaining and Hilbert Schemes
A note on commuting pairs of matrices
Géométrie des points épais
Associated graded algebra of a Gorenstein Artin algebra
Polynomials and the exponent of matrix multiplication
On degeneration of tensors and algebras
Multigraded Hilbert schemes
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Smoothable Gorenstein Points Via Marked Schemes and Double-generic Initial Ideals
On the tangent space to the Hilbert scheme of points in 𝐏³
Modules over algebraic cobordism
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Gromov–Witten theory and Donaldson–Thomas theory, I
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Multiplying matrices faster than coppersmith-winograd
The compactified jacobian can be nonreduced
Algebraic Families on an Algebraic Surface

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