Quasi elementary contractions of Fano manifolds

Details Quasi elementary contractions of Fano manifolds Quasi elementary contractions of Fano manifolds

2007-04-30

arxiv.org/abs/0704.3912v2

Mathematics

Algebraic Geometry

Final version, minor changes, to appear in Compositio Mathematica

Scientific paper

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 bounds on rho(X) when dim(X)=4 and X has a quasi elementary contraction, and other applications in higher dimensions.

Affiliated with

Also associated with

No associations

Rating

Quasi elementary contractions of Fano manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quasi elementary contractions of Fano manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quasi elementary contractions of Fano manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-415267