Geometry of the genus 9 Fano 4-folds
[Géométrie des variété de Fano de dimension 4 et genre 9]
Han, Frédéric1
1 Université Paris 7 Institut de Mathématiques de Jussieu Case Postale 7012 Bâtiment Chevaleret 75205 Paris Cedex 13 (France)
Annales de l'Institut Fourier, Tome 60 (2010) no. 4, pp. 1401-1434.

On étudie la géométrie d’une variété générale de Fano de dimension quatre, de genre neuf, et de nombre de Picard un. On calcule son anneau de Chow, et l’on donne une description simple et explicite de sa variété des droites. On utilise alors ces résultats pour étudier des propriétés géométriques de variétés de dimension 3 non quadratiquement normales dans un espace projectif de dimension cinq.

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.

DOI : 10.5802/aif.2559
Classification : 14J45, 14J35, 14J60, 14J30, 14M15, 14M07
Keywords: Fano manifold, variety of lines, secant variety, quadratic normality, vector bundles, virtual section, symplectic grassmannian
Mot clés : variété de Fano, variété des droites, variété de secantes, normalité quadratique, fibré vectoriel, section virtuelle, Grassmannienne symplectique
Han, Frédéric 1

1 Université Paris 7 Institut de Mathématiques de Jussieu Case Postale 7012 Bâtiment Chevaleret 75205 Paris Cedex 13 (France) 
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Han, Frédéric. Geometry of the genus 9 Fano 4-folds. Annales de l'Institut Fourier, Tome 60 (2010) no. 4, pp. 1401-1434. doi : 10.5802/aif.2559. http://www.numdam.org/articles/10.5802/aif.2559/

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