A study of singularities on rational curves via syzygies

DOI10.1090/S0065-9266-2012-00674-5zbMath1305.14014arXiv1102.5072OpenAlexW2093985642MaRDI QIDQ4979156

Andrew R. Kustin, David A. Cox, Claudia Polini, Bernd Ulrich

Publication date: 17 June 2014

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.5072

zbMATH Keywords

singularitiesrational curveHilbert-burch matrixrational plane quartics

Mathematics Subject Classification ID

Multiplicity theory and related topics (13H15) Plane and space curves (14H50) Families, moduli of curves (algebraic) (14H10) Computational aspects of algebraic curves (14Q05) Singularities of curves, local rings (14H20)

Related Items (20)

Strata of rational space curves ⋮ Singular rational curves with points of nearly-maximal weight ⋮ Rational plane curves parameterizable by conics ⋮ The bi-graded structure of symmetric algebras with applications to Rees rings ⋮ Linearly presented perfect ideals of codimension 2 in three variables ⋮ Survey on the theory and applications of \(\mu\)-bases for rational curves and surfaces ⋮ Singularities of plane rational curves via projections ⋮ An \(\mathrm{SL}(3, \mathbb{C})\)-equivariant smooth compactification of moduli space of rational quartic plane curves ⋮ Implicitization of rational hypersurfaces via linear syzygies: a practical overview ⋮ Strata of vector spaces of forms in \({R = \mathsf k[x, y}\), and of rational curves in \({\mathbb{P}^k}\)] ⋮ Syzygies and projective generation of plane rational curves ⋮ Rees algebras of square-free monomial ideals ⋮ Injective linear series of algebraic curves on quadrics ⋮ The explicit minimal resolution constructed from a Macaulay inverse system ⋮ On parameterizations of plane rational curves and their syzygies ⋮ Artinian Gorenstein algebras with linear resolutions ⋮ Freeness and invariants of rational plane curves ⋮ The Rees algebra of parametric curves via liftings ⋮ Defining Equations of Blowup Algebras ⋮ Remarks on double points of plane curves

Uses Software

• CASA

Cites Work

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• Matrix-based implicit representations of rational algebraic curves and applications
• Axial moving lines and singularities of rational planar curves
• Properties of Noetherian rings stable under general grade reduction
• Row ideals and fibers of morphisms
• Rational algebraic curves. A computer algebra approach
• On the equations of the moving curve ideal of a rational algebraic plane curve
• The Eisenbud-Koh-Stillman conjecture on linear syzygies
• On the number of minimal prime ideals in the completion of a local domain
• Computing singular points of plane rational curves
• What makes a complex exact?
• A simple proof of some generalized principal ideal theorems
• On plane rational curves and the splitting of the tangent bundle
• BLOWUPS AND FIBERS OF MORPHISMS
• Rational normal scrolls and the defining equations of Rees algebras
• A Note on the Multiplicity of Cohen-Macaulay Algebras with Pure Resolutions
• The restricted tangent bundle of a rational curve in P²
• A Stratification of the Space of Plane Quartic Curves
• The Geometry of Syzygies
• The Restricted Tangent Bundle of a Rational Curve on a Quadric in P 3
• Geometry of quartic curves

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