Quasi elementary contractions of Fano manifolds

@article{Casagrande2007QuasiEC,
  title={Quasi elementary contractions of Fano manifolds},
  author={C. Casagrande},
  journal={arXiv: Algebraic Geometry},
  year={2007}
}
  • C. Casagrande
  • Published 2007
  • Mathematics
  • arXiv: Algebraic Geometry
  • Let X be a smooth complex Fano variety. We define and study 'quasi elementary' contractions of fiber type f: X -> Y. These have the property that rho(X) is at most rho(Y)+rho(F), where rho is the Picard number and F is a general fiber of f. In particular any elementary extremal contraction of fiber type is quasi elementary. We show that if Y has dimension at most 3 and Picard number at least 4, then Y is smooth and Fano; if moreover rho(Y) is at least 6, then X is a product. This yields sharp… CONTINUE READING
    20 Citations
    Non-elementary Fano conic bundles.
    • 7
    • PDF
    On the Picard number of divisors in Fano manifolds
    • 24
    • PDF
    On the birational geometry of Fano 4-folds
    • 17
    • PDF
    On some Fano manifolds admitting a rational fibration
    • C. Casagrande
    • Mathematics, Computer Science
    • J. Lond. Math. Soc.
    • 2014
    • 3
    • PDF
    Numerical invariants of Fano 4-folds
    • 6
    • PDF
    Non-elementary Fano conic bundles
    • 2

    References