Fibers of generic projections

DOI10.1112/S0010437X09004503zbMath1189.14061arXiv0806.1928MaRDI QIDQ3552180

David Eisenbud, Roya Beheshti

Publication date: 13 April 2010

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0806.1928

zbMATH Keywords

linear projectionsdegree and complexity of fiberssecant lemma

Mathematics Subject Classification ID

Integral closure of commutative rings and ideals (13B22) Projective techniques in algebraic geometry (14N05) Deformations of singularities (14B07)

Related Items (12)

A note on special cubic fourfolds of small discriminants ⋮ Regularity Bounds by Projection ⋮ On the degree of algebraic cycles on hypersurfaces ⋮ Measures of irrationality for hypersurfaces of large degree ⋮ A new Castelnuovo bound for codimension three subvarieties ⋮ Equivalent birational embeddings. II: Divisors ⋮ On the smooth locus of aligned Hilbert schemes, the \(k\)-secant lemma and the general projection theorem ⋮ Classification and geometric properties of surfaces with property \(\mathbf{N}_{3,3}\) ⋮ SUPERFICIAL FIBRES OF GENERIC PROJECTIONS ⋮ Graded mapping cone theorem, multisecants and syzygies ⋮ On the size and local equations of fibres of general projections ⋮ Unobstructedness of filling secants and the Gruson-Peskine general projection theorem

Uses Software

• Macaulay2

Cites Work

• Linear free resolutions and minimal multiplicity
• On a theorem of Castelnuovo, and the equations defining space curves
• Liaison and deformation
• A sharp Castelnuovo bound for smooth surfaces
• The (dimension \(+2\))-secant lemma
• Liaison des variétés algébriques. I
• Generic projections, the equations defining projective varieties and Castelnuovo regularity
• Ideals generated by \(R\)-sequences
• Singularities of differentiable maps
• Reducibility of the families of O-dimensional schemes on a variety
• Generic projections
• Reye Congruences
• Vanishing Theorems, A Theorem of Severi, and the Equations Defining Projective Varieties
• Reye Constructions for Nodal Enriques Surfaces
• Varieties of small codimension in projective space
• Algebra Structures for Finite Free Resolutions, and Some Structure Theorems for Ideals of Codimension 3
• Examples of Smooth Non-General Type Surfaces in P⁴
• Generic Projections of Algebraic Varieties
• A Note on Gorenstein Rings of Embedding Codimension Three

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