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Classification of Fano 4-folds with Lefschetz defect 3 and Picard number 5. (English) Zbl 1469.14086

Summary: Let \(X\) be a smooth, complex Fano 4-fold, and \(\rho_X\) its Picard number. If \(X\) contains a prime divisor \(D\) with \(\rho_X-\rho_D>2\), then either \(X\) is a product of del Pezzo surfaces, or \(\rho_X=5,6\). In this setting, we completely classify the case where \(\rho_X=5\); there are 6 families, among which one is new. We also deduce the classification of Fano 4-folds with \(\rho_X\geq 5\) with an elementary divisorial contraction sending a divisor to a curve.

MSC:

14J45 Fano varieties
14J35 \(4\)-folds
14E30 Minimal model program (Mori theory, extremal rays)
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References:

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