scholarly journals Measures of irrationality of the Fano surface of a cubic threefold

2018 ◽  
Vol 371 (10) ◽  
pp. 7111-7133 ◽  
Author(s):  
Frank Gounelas ◽  
Alexis Kouvidakis
Keyword(s):  
Cubic Threefold

scholarly journals Troisi\`eme groupe de cohomologie non ramifi\'ee d'un solide cubique sur un corps de fonctions d'une variable

2018 ◽  
Vol Volume 2 ◽  
Author(s):  
Jean-Louis Colliot-Thélène ◽  
Alena Pirutka
Keyword(s):  
Function Field ◽  
Cohomology Group ◽  
Chow Group ◽  
Hodge Conjecture ◽  
Complex Curve ◽  
The Third ◽  
Generic Fibre ◽  
Nous Montrons ◽  
Unramified Cohomology ◽  
Cubic Threefold

En combinant une m\'ethode de C. Voisin avec la descente galoisienne sur le groupe de Chow en codimension $2$, nous montrons que le troisi\`eme groupe de cohomologie non ramifi\'ee d'un solide cubique lisse d\'efini sur le corps des fonctions d'une courbe complexe est nul. Ceci implique que la conjecture de Hodge enti\`ere pour les classes de degr\'e 4 vaut pour les vari\'et\'es projectives et lisses de dimension 4 fibr\'ees en solides cubiques au-dessus d'une courbe, sans restriction sur les fibres singuli\`eres. --------------- We prove that the third unramified cohomology group of a smooth cubic threefold over the function field of a complex curve vanishes. For this, we combine a method of C. Voisin with Galois descent on the codimension $2$ Chow group. As a corollary, we show that the integral Hodge conjecture holds for degree $4$ classes on smooth projective fourfolds equipped with a fibration over a curve, the generic fibre of which is a smooth cubic threefold, with arbitrary singularities on the special fibres. Comment: in French

scholarly journals The Intermediate Jacobian of the Cubic Threefold

1972 ◽  
Vol 95 (2) ◽  
pp. 281 ◽  
Author(s):  
C. Herbert Clemens ◽  
Phillip A. Griffiths
Keyword(s):  
Cubic Threefold ◽  
Intermediate Jacobian

Weak Fano bundles on the cubic threefold

2015 ◽  
Vol 149 (1-2) ◽  
pp. 171-177
Author(s):  
Daizo Ishikawa
Keyword(s):  
Cubic Threefold ◽  
Weak Fano

scholarly journals MINIMAL CLASSES ON THE INTERMEDIATE JACOBIAN OF A GENERIC CUBIC THREEFOLD

2010 ◽  
Vol 12 (01) ◽  
pp. 55-70 ◽  
Author(s):  
ANDREAS HÖRING
Keyword(s):  
Cohomology Class ◽  
Cubic Threefold ◽  
Intermediate Jacobian

Let X be a smooth cubic threefold. We can associate two objects to X: the intermediate Jacobian J and the Fano surface F parametrizing lines on X. By a theorem of Clemens and Griffiths, the Fano surface can be embedded in the intermediate Jacobian and the cohomology class of its image is minimal. In this paper, we show that if X is generic, the Fano surface is the only surface of minimal class in J.

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