Geometry of the genus 9 Fano 4-folds

Han, Frédéric

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.

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

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