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arXiv · 1803.09129

A characterization of some Fano 4-folds through conic fibrations

Pedro Montero·Eleonora Anna Romano
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Abstract

We find a characterization for Fano 4-folds $X$ with Lefschetz defect $\delta_{X}=3$: besides the product of two del Pezzo surfaces, they correspond to varieties admitting a conic bundle structure $f\colon X\to Y$ with $\rho_{X}-\rho_{Y}=3$. 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 $\delta_{X}=3$.

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Pedro Montero, Eleonora Anna Romano. 2018-03-24. A characterization of some Fano 4-folds through conic fibrations. https://arxiv.org/abs/1803.09129

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