# A characterization of some Fano 4-folds through conic fibrations

@article{Montero2018ACO, title={A characterization of some Fano 4-folds through conic fibrations}, author={P. Montero and E. Romano}, journal={arXiv: Algebraic Geometry}, year={2018} }

Let $X$ be a complex projective Fano $4$-fold. Let $D\subset X$ be a prime divisor. Let us consider the image $\mathcal{N}_{1}(D,X)$ of $\mathcal{N}_{1}(D)$ in $\mathcal{N}_{1}(X)$ through the natural push-forward of one-cycles. Let us consider the following invariant of $X$ given by $\delta_{X}:=\max\{\operatorname{codim} \mathcal{N}_{1}(D,X)\;|\;D\subset X \text{ prime divisor} \}$, called Lefschetz defect. We find a characterization for Fano 4-folds with $\delta_{X}=3$: besides the productâ€¦Â CONTINUE READING

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