Grassmann defective surfaces

Claudio Fontanari

Bollettino dell'Unione Matematica Italiana (2004)

  • Volume: 7-B, Issue: 2, page 369-379
  • ISSN: 0392-4041

Abstract

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A projective variety V is 1 , h -defective if the Grassmannian of lines contained in the span of h + 1 independent points on V has dimension less than the expected one. In the present paper, which is inspired by classical work of Alessandro Terracini, we prove a criterion of 1 , h -defectivity for algebraic surfaces and we discuss its applications to Veronese embeddings and to rational normal scrolls.

How to cite

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Fontanari, Claudio. "Grassmann defective surfaces." Bollettino dell'Unione Matematica Italiana 7-B.2 (2004): 369-379. <http://eudml.org/doc/195075>.

@article{Fontanari2004,
abstract = {A projective variety $V$ is $(1, h)$-defective if the Grassmannian of lines contained in the span of $h+1$ independent points on $V$ has dimension less than the expected one. In the present paper, which is inspired by classical work of Alessandro Terracini, we prove a criterion of $(1, h)$-defectivity for algebraic surfaces and we discuss its applications to Veronese embeddings and to rational normal scrolls.},
author = {Fontanari, Claudio},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {369-379},
publisher = {Unione Matematica Italiana},
title = {Grassmann defective surfaces},
url = {http://eudml.org/doc/195075},
volume = {7-B},
year = {2004},
}

TY - JOUR
AU - Fontanari, Claudio
TI - Grassmann defective surfaces
JO - Bollettino dell'Unione Matematica Italiana
DA - 2004/6//
PB - Unione Matematica Italiana
VL - 7-B
IS - 2
SP - 369
EP - 379
AB - A projective variety $V$ is $(1, h)$-defective if the Grassmannian of lines contained in the span of $h+1$ independent points on $V$ has dimension less than the expected one. In the present paper, which is inspired by classical work of Alessandro Terracini, we prove a criterion of $(1, h)$-defectivity for algebraic surfaces and we discuss its applications to Veronese embeddings and to rational normal scrolls.
LA - eng
UR - http://eudml.org/doc/195075
ER -

References

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  1. CASANELLAS I RIUS, M., Teoria de liaison en codimensió arbitrària, PhD Thesis (Universitat de Barcelona). 
  2. CHIANTINI, L.- CILIBERTO, C., Weakly defective varieties, Trans. Amer. Math. Soc., 354 (2002), 151-178. Zbl1045.14022MR1859030
  3. CHIANTINI, L.- COPPENS, M., Grassmannians of secant varieties, Forum Math., 13 (2001), 615-628. Zbl1033.14033MR1858491
  4. CILIBERTO, C., Superficie algebriche complesse: idee e metodi della classificazione, Atti del convegno di Geometria Algebrica, Genova-Nervi, 12-17 aprile 1984, 39-157. 
  5. CILIBERTO, C., Geometric Aspects of Polynomial Interpolation in More Variables and of Waring's Problem, European Congress of Mathematics, Vol. I (Barcelona, 2000), 289-316. Zbl1078.14534MR1905326
  6. CILIBERTO, C.- HIRSCHOWITZ, A., Hypercubique de P 4 avec sept points singuliers generiques, C. R. Acad. Sci. Paris, 313 I (1991), 135-137. Zbl0746.14001MR1121575
  7. CILIBERTO, C.- LOPEZ, A. F., On the existence of components of the Noether-Lefschetz locus with given codimension, Manuscripta Math., 73 (1991), 341-357. Zbl0769.14018MR1134567
  8. DIONISI, C.- FONTANARI, C., Grassmann defectivity à la Terracini, Le Matematiche, LVI (2001), 245-255. Zbl1177.14093MR2009896
  9. LONDON, F., Ueber die Polarfiguren der ebenen Kurven dritter Ordnung, Math. Ann., 36 (1890). MR1510635JFM22.0735.03
  10. TERRACINI, A., Sulla rappresentazione delle coppie di forme ternarie mediante somme di potenze di forme lineari, Ann. di Matem. pura ed appl., XXIV, III (1915), 91-100. JFM45.0239.01

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