On Landsberg's criterion for complete intersections
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TL;DR: In this article, an elementary proof of Landsberg's criterion that is valid over any ground field is given, since they do not assume the variety in question to be irreducible.
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Abstract: In his paper [1] J.M. Landsberg proves, among others, an elementary characterization of complete intersections [1, Proposition 1.2; see also Proposition 1.3 below]. The proof of this proposition uses method of moving frames. The aim of this note is to give an elementary proof of Landsberg's criterion that is valid over any ground field. In fact, we prove a little more, since we do not assume the variety in question to be irreducible. A preliminary version of this note was posted as an eprint at publicat ions.math.duke.edu/alg-geom/9408006. The author is grateful to J.M. Landsberg for his concern and useful correspondence and to the referee for useful suggestions.
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Citations
•Book
Cartan for beginners
Thomas A. Ivey,Joseph M. Landsberg +1 more
- 01 Jan 2003
TL;DR: In this article, Cartan-Kahler et al. present the Cartan algorithm for linear Pfaffian systems for moving frames and exterior differential systems in projective geometry.
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Algebraic geometry and projective differential geometry, Seoul National University concentrated lecture series, 1997
Abstract: This is an expanded and updated version of a lecture series I gave at Seoul National University in September 1997. It is in some sense an update of the 1979 Griffiths and Harris paper with a similar title. I discuss:
Homogeneous varieties, Topology and consequences Projective differential invariants, Varieties with degenerate Gauss images, When can a uniruled variety be smooth?, Dual varieties, Linear systems of bounded and constant rank, Secant and tangential varieties, Systems of quadrics with tangential defects, Recognizing uniruled varieties, Recognizing intersections of quadrics, Recognizing homogeneous spaces, Complete intersections.
This is a preliminary version, so please send me comments, corrections and questions.
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On the local differential geometry of complete intersections
Joseph M. Landsberg
- 01 Jan 1995
TL;DR: In this paper, the Séminaire de Théorie spectrale et géométrie implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.php).
Cartan for Beginners: Differential Geometry via Moving Frames and Exterior Differential Systems, Second Edition
Thomas A. Ivey,Joseph M. Landsberg +1 more
- 15 Dec 2016
TL;DR: In this article, the Frobenius Theorem p.6.14.6 should begin with a connected Lie group and displayed equation should read dωe(X,Y ) = −[X, Y ] (not +)
References
Geometry of algebraic curves
Enrico Arbarello,Maurizio Cornalba,Phillip Griffiths,Joe Harris +3 more
- 01 Jan 1985
TL;DR: This chapter discusses Brill-Noether theory on a moving curve, and some applications of that theory in elementary deformation theory and in tautological classes.
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Differential-geometric characterizations of complete intersections
TL;DR: In this article, a sufficient condition for a complete intersection to be testable at any smooth point of a projective variety X ∈ CPn+a was derived. But the sufficient condition has a geometric interpretation in terms of restrictions on the spaces of osculating hypersurfaces at x.
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