Geodesic
Minimal sections of conic bundles
Bollettino della Unione matematica italiana, Série 8, 2B (1999) no. 2, pp. 401-428.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

Sia $p : X \to P^{2}$ un fibrato in coniche standard con curva discriminante $\Delta$ di grado $d$. La varietà delle sezioni minime delle superfici $p^{-1}(C)$, dove $C$ è una curva di grado $d-3$, si spezza in due componenti $\mathcal{C}_{+}$ e $\mathcal{C}_{-}$. Si prova che, mediante la mappa di Abel-Jacobi $\Phi$, una di queste componenti domina la Jacobiana intermedia $JX$, mentre l'altra domina il divisore theta $\Theta\subset JX$. Questi risultati vengono applicati ad alcuni threefold di Fano birazionalmente equivalenti a un fibrato in coniche. In particolare si prova che il generico threefold di Fano di grado dieci è birazionale a una ipersuperficie di tipo $(2, 2)$ nel prodotto di Segre di due piani proiettivi. 
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Iliev, Atanas. Minimal sections of conic bundles. Bollettino della Unione matematica italiana, Série 8, 2B (1999) no. 2, pp. 401-428. http://geodesic.mathdoc.fr/item/BUMI_1999_8_2B_2_a16/

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