On the smooth locus of aligned Hilbert schemes, the \(k\)-secant lemma and the general projection theorem

DOI10.1215/00127094-2019817zbMath1262.14058arXiv1010.2399OpenAlexW2949393036WikidataQ124829635 ScholiaQ124829635MaRDI QIDQ1942108

Christian Peskine, Laurent Gruson

Publication date: 15 March 2013

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.2399

zbMATH Keywords

Hilbert schemes\(k\)-secantsgeneral projections

Mathematics Subject Classification ID

Projective techniques in algebraic geometry (14N05) Low codimension problems in algebraic geometry (14M07)

Related Items (8)

Measures of irrationality for hypersurfaces of large degree ⋮ Le Potier's strange duality, quot schemes, and multiple point formulas for del Pezzo surfaces ⋮ A new Castelnuovo bound for codimension three subvarieties ⋮ Trisecant flops, their associated \(K3\) surfaces and the rationality of some cubic fourfolds ⋮ SUPERFICIAL FIBRES OF GENERIC PROJECTIONS ⋮ The relative Hilbert scheme of projection morphisms ⋮ On the size and local equations of fibres of general projections ⋮ Unobstructedness of filling secants and the Gruson-Peskine general projection theorem

Cites Work

• The (dimension \(+2\))-secant lemma
• The theorem of Mather on generic projections in the setting of algebraic geometry
• Complex surfaces and connected sums of complex projective planes
• The smooth surfaces in \({\mathbb{P}}^ 4\) without apparent triple points
• The multiple-point schemes of a finite curvilinear map of codimension one
• Generic projections
• Fibers of generic projections
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