Curves of degree \(r+2\) in \(\mathbb{P}^r\): Cohomological, geometric, and homological aspects

DOI10.1006/jabr.2001.8847zbMath1031.14013OpenAlexW2038596749MaRDI QIDQ5945127

Markus P. Brodmann, Peter Schenzel

Publication date: 26 February 2004

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.2001.8847

zbMATH Keywords

codimensionrational normal curveBetti numersCastelnuovo regularityelliptic normal curveHartshorne-Rao modulehomogeneous coordinate ring

Mathematics Subject Classification ID

Plane and space curves (14H50) Special algebraic curves and curves of low genus (14H45) Classical real and complex (co)homology in algebraic geometry (14F25) Low codimension problems in algebraic geometry (14M07)

Related Items (7)

Arithmetic properties of projective varieties of almost minimal degree ⋮ On varieties of almost minimal degree in small codimension ⋮ Projective surfaces of degree \(r+1\) in projective \(r\)-space and almost non-singular projections ⋮ Projective subvarieties having large Green-Lazarsfeld index ⋮ Projective curves with maximal regularity and applications to syzygies and surfaces ⋮ Projective curves of degree=codimension+2 ⋮ Defining Equations of Rational Curves in Smooth Quadric Surface

Uses Software

• Macaulay2

Cites Work

• On Veronesean embeddings and projections of Veronesean varieties
• Koszul cohomology and the geometry of projective varieties. Appendix: The nonvanishing of certain Koszul cohomology groups (by Mark Green and Robert Lazarsfeld)
• On a theorem of Castelnuovo, and the equations defining space curves
• Bounds on the cohomological Hilbert functions of a projective variety
• On the complexity of computing syzygies
• Über die freien Auflösungen extremaler Cohen-Macaulay-Ringe
• The genus of space curves
• Towards a structure theory for projective varieties of degree = codimension + 2
• On the minimal free resolution of \(r+3\) points in projective \(r\)-space
• Nondegenerate surfaces of degree n+3 in PnC.
• On Singular Curves in the Case of Positive Characteristic
• Bounds for the cohomology and the Castelnuovo regularity of certain surfaces
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