Geometry of the genus 9 Fano 4-folds

Frédéric Han[1]

  • [1] Université Paris 7 Institut de Mathématiques de Jussieu Case Postale 7012 Bâtiment Chevaleret 75205 Paris Cedex 13 (France)

Annales de l’institut Fourier (2010)

  • Volume: 60, Issue: 4, page 1401-1434
  • ISSN: 0373-0956

Abstract

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We study the geometry of a general Fano variety of dimension four, genus nine, and Picard number one. We compute its Chow ring and give an explicit description of its variety of lines. We apply these results to study the geometry of non quadratically normal varieties of dimension three in a five dimensional projective space.

How to cite

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Han, Frédéric. "Geometry of the genus 9 Fano 4-folds." Annales de l’institut Fourier 60.4 (2010): 1401-1434. <http://eudml.org/doc/116308>.

@article{Han2010,
abstract = {We study the geometry of a general Fano variety of dimension four, genus nine, and Picard number one. We compute its Chow ring and give an explicit description of its variety of lines. We apply these results to study the geometry of non quadratically normal varieties of dimension three in a five dimensional projective space.},
affiliation = {Université Paris 7 Institut de Mathématiques de Jussieu Case Postale 7012 Bâtiment Chevaleret 75205 Paris Cedex 13 (France)},
author = {Han, Frédéric},
journal = {Annales de l’institut Fourier},
keywords = {Fano manifold; variety of lines; secant variety; quadratic normality; vector bundles; virtual section; symplectic grassmannian; vector bundle; family of lines; symplectic Grassmannian},
language = {eng},
number = {4},
pages = {1401-1434},
publisher = {Association des Annales de l’institut Fourier},
title = {Geometry of the genus 9 Fano 4-folds},
url = {http://eudml.org/doc/116308},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Han, Frédéric
TI - Geometry of the genus 9 Fano 4-folds
JO - Annales de l’institut Fourier
PY - 2010
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 4
SP - 1401
EP - 1434
AB - We study the geometry of a general Fano variety of dimension four, genus nine, and Picard number one. We compute its Chow ring and give an explicit description of its variety of lines. We apply these results to study the geometry of non quadratically normal varieties of dimension three in a five dimensional projective space.
LA - eng
KW - Fano manifold; variety of lines; secant variety; quadratic normality; vector bundles; virtual section; symplectic grassmannian; vector bundle; family of lines; symplectic Grassmannian
UR - http://eudml.org/doc/116308
ER -

References

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