A stratification of the Hilbert scheme of points in the projective plane

DOI10.1007/BF01161642zbMath0637.14003MaRDI QIDQ1098899

Gerd Gotzmann

Publication date: 1988

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/173985

zbMATH Keywords

Hilbert functionstratification of Hilbert scheme of the projective plane

Mathematics Subject Classification ID

Homogeneous spaces and generalizations (14M17) Parametrization (Chow and Hilbert schemes) (14C05) Projective techniques in algebraic geometry (14N05)

Related Items

On the Stratification of Nested Hilbert Schemes ⋮ Families of Artinian and one-dimensional algebras ⋮ Canonical Hilbert-Burch matrices for ideals of \(k[x,y\)] ⋮ Families of Artinian and low dimensional determinantal rings ⋮ The scheme of liftings and applications ⋮ Parametrizations of ideals in \(K[x,y\) and \(K[x,y,z]\)] ⋮ Some irreducible Hilbert schemes ⋮ Maximal families of superabundant point systems in \(\mathbb{P}^ 2\) ⋮ Families of low dimensional determinantal schemes ⋮ Ideal classes of three dimensional Artin-Schelter regular algebras. ⋮ Betti strata of height two ideals ⋮ The Family G_Tof Graded Artinian Quotients ofk[x,y of Given Hilbert Function] ⋮ On incidence between strata of the Hilbert scheme of points on \(\mathbb{P}^{2}\) ⋮ Identifying limits of ideals of points in the case of projective space ⋮ Foliations on \(\mathbb{CP}^2\) with a unique singular point without invariant algebraic curves ⋮ Connectedness of Hilbert function strata and other connectedness results ⋮ On the reducibility of the postulation Hilbert scheme ⋮ Einfacher Zusammenhang der Hilbertschemata von Kurven im komplex-projektiven Raum. (Simple connectedness of the Hilbert schemes of curves in complex projective space)

Cites Work

• A criterion for detecting m-regularity
• On the homology of the Hilbert scheme of points in the plane
• Durch Hilbertfunktionen definierte Unterschemata des Hilbertschemas. (Subschemes of the Hilbert scheme defined by Hilbert functions)
• Some theorems on actions of algebraic groups
• Punctual Hilbert schemes
• Algebraic Families on an Algebraic Surface
• Lectures on Curves on an Algebraic Surface. (AM-59)