Quasi elementary contractions of Fano manifolds

  title={Quasi elementary contractions of Fano manifolds},
  author={C. Casagrande},
  journal={arXiv: Algebraic Geometry},
  • 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
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