A characterization of some Fano 4folds through conic fibrations
Abstract
We find a characterization for Fano 4folds $X$ 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 $\delta_{X}=3$.
 Publication:

arXiv eprints
 Pub Date:
 March 2018
 arXiv:
 arXiv:1803.09129
 Bibcode:
 2018arXiv180309129M
 Keywords:

 Mathematics  Algebraic Geometry;
 14E08;
 14E30;
 14J35;
 14J45
 EPrint:
 21 pages. v2: major revision