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 >= 5 with an elementary divisorial contraction sending a divisor to a curve. (C) 2021 Elsevier B.V. All rights reserved.
Classification of Fano 4-folds with Lefschetz defect 3 and Picard number 5
Romano, EA
2022-01-01
Abstract
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 >= 5 with an elementary divisorial contraction sending a divisor to a curve. (C) 2021 Elsevier B.V. All rights reserved.
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