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}
}
  • P. Montero, E. Romano
  • Published 2018
  • Mathematics
  • arXiv: Algebraic Geometry
  • 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 product… CONTINUE READING
    3 Citations

    Figures from this paper

    Classification of Fano 4-folds with Lefschetz defect 3 and Picard number 5.
    • PDF
    On some Fano 4-folds with Lefschetz defect 3
    • PDF
    A note on flatness of some fiber type contractions.
    • 1
    • PDF

    References

    SHOWING 1-10 OF 33 REFERENCES
    Around the Mukai conjecture for Fano manifolds
    • 2
    • PDF
    Non-elementary Fano conic bundles.
    • 7
    • PDF
    On the Picard number of divisors in Fano manifolds
    • 24
    • PDF
    On the Picard number of singular Fano varieties
    • 12
    • PDF
    On the classification of toric Fano 4-folds
    • 125
    • PDF
    Quasi elementary contractions of Fano manifolds
    • 20
    • PDF
    Toward the classification of higher-dimensional toric Fano varieties
    • 105
    • PDF
    Mori dream spaces and GIT.
    • 373
    • PDF
    Decomposition of Toric Morphisms
    • 189