Gröbner cells of punctual Hilbert schemes in dimension two
DOI10.1016/j.jalgebra.2022.01.012zbMath1487.14012arXiv2005.05759OpenAlexW4210422310MaRDI QIDQ2075935
Publication date: 16 February 2022
Published in: Journal of Algebra (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2005.05759
zeta functionsHilbert schemesaffine planeplane curve singularitiesGröbner cellsGrothendieck-Deligne map
Exact enumeration problems, generating functions (05A15) Combinatorial aspects of representation theory (05E10) Hecke algebras and their representations (20C08) Singularities in algebraic geometry (14B05) Braid groups; Artin groups (20F36) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Plane and space curves (14H50) Parametrization (Chow and Hilbert schemes) (14C05) Jacobians, Prym varieties (14H40) Singularities of curves, local rings (14H20) Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- DAHA and iterated torus knots
- A support theorem for Hilbert schemes of planar curves
- Refined knot invariants and Hilbert schemes
- S-duality for surfaces with \(A_n\)-type singularities
- On the homology of the Hilbert scheme of points in the plane
- DAHA and plane curve singularities
- The Hilbert scheme of a plane curve singularity and the \textsc{HOMFLY} homology of its link
- Euler characteristics of Hilbert schemes of points on simple surface singularities
- Macdonald formula for curves with planar singularities
- Canonical Hilbert-Burch matrices for ideals of \(k[x,y\)]
- Analytic classification of plane branches up to multiplicity 4
- The Betti numbers of the Hilbert scheme of points on a smooth projective surface
- Reduced Hilbert schemes for irreducible curve singularities
- Description de Hilb sup(n) C{X,Y}
- Local and global zeta-functions of singular algebraic curves
- Hilbert schemes of zero-dimensional subschemes of smooth varieties
- Heisenberg algebra and Hilbert schemes of points on projective surfaces
- \(t,q\)-Catalan numbers and the Hilbert scheme.
- Modules over plane curve singularities in any ranks and DAHA
- Compactified Jacobians and \(q,t\)-Catalan numbers. I.
- Riemann hypothesis for DAHA superpolynomials and plane curve singularities
- Counting the ideals of given codimension of the algebra of Laurent polynomials in two variables
- Parametrizations of ideals in \(K[x,y\) and \(K[x,y,z]\)]
- Compactified Jacobians and \(q,t\)-Catalan numbers. II
- Topology of the compactified Jacobians of singular curves
- Hilbert schemes, polygraphs and the Macdonald positivity conjecture
- Punctual Hilbert schemes
- Euler Characteristics of Hilbert Schemes of Points On Surfaces with Simple Singularities