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Casagrande, Cinzia:
On some numerical properties of Fano varieties
Bollettino dell'Unione Matematica Italiana Serie 8 7-B (2004), fasc. n.3, p. 663-671, Unione Matematica Italiana (English)
pdf (240 Kb), djvu (133 Kb). | MR238489 | Zbl 1110.14034

Sunto

Questa nota è il testo di una conferenza tenuta al XVII Convegno dell'Unione Matematica Italiana, tenutosi a Milano, 8-13 settembre 2003. Parlo di alcune congetture e teoremi sulle relazioni tra l'indice, lo pseudo-indice e il numero di Picard di una varietà di Fano. I risultati in questione fanno parte di un lavoro in collaborazione con Bonavero, Debarre e Druel.
Referenze Bibliografiche
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[Bat99] VICTOR V. BATYREV, On the classification of toric Fano 4-folds, Journal of Mathematical Sciences (New York), 94 (1999), 1021-1050. | MR 1703904 | Zbl 0929.14024
[BCDD03] LAURENT BONAVERO-CINZIA CASAGRANDE-OLIVIER DEBARRE-STÉPHANE DRUEL, Sur une conjecture de Mukai, Commentarii Mathematici Helvetici, 78 (2003), 601-626. | MR 1998396 | Zbl 1044.14019
[Bon03] LAURENT BONAVERO, Pseudo-index of Fano manifolds and smooth blowups, preprint math.AG/0309460, 2003. | fulltext mini-dml | Zbl 1081.14056
[Cas03a] CINZIA CASAGRANDE, Contractible classes in toric varieties, Mathematische Zeitschrift, 243 (2003), 99-126. | MR 1953051 | Zbl 1077.14070
[Cas03b] CINZIA CASAGRANDE, Toric Fano varieties and birational morphisms, International Mathematics Research Notices, 27 (2003), 1473-1505. | MR 1976232 | Zbl 1083.14516
[CMSB02] KOJI CHO-YOICHI MIYAOKA-NICK SHEPHERD-BARRON, Characterizations of projective space and applications to complex symplectic geometry. In Higher Dimensional Birational Geometry, volume 35 of Advanced Studies in Pure Mathematics, 1-89, Mathematical Society of Japan, 2002. | MR 1929791 | Zbl 1063.14065
[Deb03] OLIVIER DEBARRE, Fano varieties. In Higher Dimensional Varieties and Rational Points (Budapest, 2001), volume 12 of Bolyai Society Mathematical Studies, 93-132, Springer-Verlag, 2003. | MR 2011745 | Zbl 0939.14022
[IP99] VASILII A. ISKOVSKIKH-YURI G. PROKHOROV, Algebraic Geometry V - Fano Varieties, volume 47 of Encyclopaedia of Mathematical Sciences, Springer-Verlag, 1999. | MR 1668579
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[Occ03] GIANLUCA OCCHETTA, A characterization of products of projective spaces, Preprint, available at the author's web page http://www.science.unitn.it/~occhetta/mainh.hmtl, 2003. | MR 2226250 | Zbl 1115.14034
[Oda88] TADAO ODA, Convex Bodies and Algebraic Geometry - An Introduction to the Theory of Toric Varieties, volume 15 of Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer-Verlag, 1988. | MR 922894 | Zbl 0628.52002
[Sat00] HIROSHI SATO, Toward the classification of higher-dimensional toric Fano varieties, Tôhoku Mathematical Journal, 52 (2000), 383-413. | fulltext mini-dml | MR 1772804 | Zbl 1028.14015
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[Wiś02] JAROSLAW A. WIŚNIEWSKI, Toric Mori theory and Fano manifolds. In Geometry of Toric Varieties, volume 6 of Séminaires et Congrés, pages 249-272. Société Mathématique de France, 2002. | MR 2063740 | Zbl 1053.14002

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