• DOI:10.1112/S0010437X08003679
Corpus ID: 6513940

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

View PDF on arXiv

Save to Library

Create Alert

Cite

Launch Research Feed