scholarly journals Osculating spaces to secant varieties

2004 ◽  
Vol 53 (3) ◽  
pp. 429-436 ◽  
Author(s):  
Edoardo Ballico ◽  
Claudio Fontanari ◽  
Cristiano Bocci ◽  
Enrico Carlini
Keyword(s):  
Secant Varieties ◽  
Osculating Spaces

scholarly journals Non-defectivity of Grassmannian bundles over a curve

2016 ◽  
Vol 27 (07) ◽  
pp. 1640002 ◽  
Author(s):  
Insong Choe ◽  
George H. Hitching
Keyword(s):  
Vector Bundles ◽  
Manuscripta Math ◽  
Maximal Degree ◽  
Geometric Proof ◽  
Secant Varieties ◽  
Grassmann Bundle ◽  
Positive Rank

Let [Formula: see text] be the Grassmann bundle of two-planes associated to a general bundle [Formula: see text] over a curve [Formula: see text]. We prove that an embedding of [Formula: see text] by a certain twist of the relative Plücker map is not secant defective. This yields a new and more geometric proof of the Hirschowitz-type bound on the isotropic Segre invariant for maximal isotropic sub-bundles of orthogonal bundles over [Formula: see text], analogous to those given for vector bundles and symplectic bundles in [I. Choe and G. H. Hitching, Secant varieties and Hirschowitz bound on vector bundles over a curve, Manuscripta Math. 133 (2010) 465–477, I. Choe and G. H. Hitching, Lagrangian sub-bundles of symplectic vector bundles over a curve, Math. Proc. Cambridge Phil. Soc. 153 (2012) 193–214]. From the non-defectivity, we also deduce an interesting feature of a general orthogonal bundle of even rank over [Formula: see text], contrasting with the classical and symplectic cases: a general maximal isotropic sub-bundle of maximal degree intersects at least one other such sub-bundle in positive rank.

scholarly journals The Hitchhiker Guide to: Secant Varieties and Tensor Decomposition

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 314 ◽  
Author(s):  
Alessandra Bernardi ◽  
Enrico Carlini ◽  
Maria Catalisano ◽  
Alessandro Gimigliano ◽  
Alessandro Oneto
Keyword(s):  
Algebraic Geometry ◽  
Projective Variety ◽  
Tensor Decomposition ◽  
Tensor Rank ◽  
Segre Variety ◽  
Secant Varieties ◽  
Open Problems ◽  
Veronese Variety ◽  
Strong Motivation

We consider here the problem, which is quite classical in Algebraic geometry, of studying the secant varieties of a projective variety X. The case we concentrate on is when X is a Veronese variety, a Grassmannian or a Segre variety. Not only these varieties are among the ones that have been most classically studied, but a strong motivation in taking them into consideration is the fact that they parameterize, respectively, symmetric, skew-symmetric and general tensors, which are decomposable, and their secant varieties give a stratification of tensors via tensor rank. We collect here most of the known results and the open problems on this fascinating subject.

scholarly journals Singularities and syzygies of secant varieties of nonsingular projective curves

2020 ◽  
Vol 222 (2) ◽  
pp. 615-665
Author(s):  
Lawrence Ein ◽  
Wenbo Niu ◽  
Jinhyung Park
Keyword(s):  
Secant Varieties ◽  
Projective Curves

scholarly journals Higher secant varieties of the minimal adjoint orbit

2004 ◽  
Vol 280 (2) ◽  
pp. 743-761 ◽  
Author(s):  
Karin Baur ◽  
Jan Draisma
Keyword(s):  
Secant Varieties ◽  
Adjoint Orbit

scholarly journals Secant varieties of the varieties of reducible hypersurfaces in Pn

2019 ◽  
Vol 528 ◽  
pp. 381-438
Author(s):  
M.V. Catalisano ◽  
A.V. Geramita ◽  
A. Gimigliano ◽  
B. Harbourne ◽  
J. Migliore ◽  
...  
Keyword(s):  
Secant Varieties

scholarly journals Secant varieties of toric varieties arising from simplicial complexes

2020 ◽  
Vol 588 ◽  
pp. 428-457
Author(s):  
M. Azeem Khadam ◽  
Mateusz Michałek ◽  
Piotr Zwiernik
Keyword(s):  
Toric Varieties ◽  
Simplicial Complexes ◽  
Secant Varieties

Osculating Spaces

1962 ◽  
Vol 14 ◽  
pp. 669-684
Author(s):  
Peter Scherk
Keyword(s):  
Duality Theorem ◽  
Characteristic Curve ◽  
Independent Interest ◽  
Natural Approach ◽  
Osculating Spaces ◽  
Analytical Tools

In this paper an attempt is made to prove some of the basic theorems on the osculating spaces of a curve under minimum assumptions. The natural approach seems to be the projective one. A duality yields the corresponding results for the characteristic spaces of a family of hyperplanes. A duality theorem for such a family and its characteristic curve also is proved. Finally the results are applied to osculating hyperspheres of curves in a conformai space.The analytical tools are collected in the first three sections. Some of them may be of independent interest.

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