A characterization of some Fano 4-folds through conic fibrations

2018/03/24 by Montero, Pedro, Romano, Eleonora Anna
#14E08 #14E30 #14J35 #14J45 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1803.09129

Abstract

We find a characterization for Fano 4-folds X with Lefschetz defect δ_X=3: besides the product of two del Pezzo surfaces, they correspond to varieties admitting a conic bundle structure f\colon X→ Y with ρ_X-ρ_Y=3. Moreover, we observe that all of these varieties are rational. We give the list of all possible targets of such contractions. Combining our results with the classification of toric Fano 4-folds due to Batyrev and Sato we provide explicit examples of Fano conic bundles from toric 4-folds with δ_X=3.

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