Minimal sections of conic bundles

Iliev, Atanas

Iliev, Atanas

Bollettino dell'Unione Matematica Italiana, Tome 2-A (1999), p. 401-428 / Harvested from Biblioteca Digitale Italiana di Matematica

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Résumé

Sia $p : X \to P^{2}$ un fibrato in coniche standard con curva discriminante $Δ$ 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 $C_{+}$ e $C_{-}$ . Si prova che, mediante la mappa di Abel-Jacobi $Φ$ , una di queste componenti domina la Jacobiana intermedia $J X$ , mentre l'altra domina il divisore theta $Θ \subset J X$ . 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.

Publié le : 1999-06-01

MR 1706556 | Zbl 0968.14019

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     author = {Atanas Iliev},
     title = {Minimal sections of conic bundles},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {2-A},
     year = {1999},
     pages = {401-428},
     zbl = {0968.14019},
     mrnumber = {1706556},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_1999_8_2B_2_401_0}
}

Iliev, Atanas. Minimal sections of conic bundles. Bollettino dell'Unione Matematica Italiana, Tome 2-A (1999) pp. 401-428. http://gdmltest.u-ga.fr/item/BUMI_1999_8_2B_2_401_0/

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