Multiplicities of a bigraded ring and intersection theory

DOI10.1007/s002080050128zbMath0894.14005OpenAlexW2057812107MaRDI QIDQ1380087

Rüdiger Achilles, Mirella Manaresi

Publication date: 13 August 1998

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

Full work available at URL: https://doi.org/10.1007/s002080050128

zbMATH Keywords

intersection theoryanalytic spreadSamuel multiplicitySegre classesBezout's theoremembedded joinStückrad-Vogel intersection cycle

Mathematics Subject Classification ID

Multiplicity theory and related topics (13H15) Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry (14C17) Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30)

Related Items (24)

On the first generalized Hilbert coefficient and depth of associated graded rings ⋮ Segre numbers, a generalized King formula, and local intersections ⋮ Generalized Hilbert coefficients and Northcott's inequality ⋮ Some extensions of Hilbert-Kunz multiplicity ⋮ Multiplicities for arbitrary modules and reduction ⋮ Nonproper intersection products and generalized cycles ⋮ Generalized Samuel Multiplicities of Monomial Ideals and Volumes ⋮ Some properties of the multiplicity sequence for arbitrary ideals ⋮ When does a perturbation of the equations preserve the normal cone? ⋮ Hilbert functions of multigraded algebras, mixed multiplicities of ideals and their applications ⋮ Multiplicity sequence and integral dependence ⋮ Generic residual intersections and intersection numbers of movable components ⋮ Mixed multiplicities, Segre numbers and Segre classes ⋮ Green functions, Segre numbers, and King's formula ⋮ Generalized Hilbert Functions ⋮ A Degree Formula for Secant Varieties of Curves ⋮ Reduction numbers of equimultiple ideals ⋮ Arithmetic degree and associated graded modules ⋮ Global representation of Segre numbers by Monge-Ampère products ⋮ On a Monge-Ampere operator for plurisubharmonic functions with analytic singularities ⋮ On the self-intersection cycle of surfaces and some classical formulas for their secant varieties ⋮ On non-proper intersections and local intersection numbers ⋮ Formulas for the multiplicity of graded algebras ⋮ A numerical characterization of the \(S_{2}\)-ification of a Rees algebra

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