On semipositivity of sheaves of differential operators and the degree of a unipolar Q-Fano variety

Details On semipositivity of sheaves of differential operators and the degree of a unipolar Q-Fano variety On semipositivity of sheaves of differential operators and the degree of a unipolar Q-Fano variety

1998-11-04

arxiv.org/abs/math/9811022v3

Mathematics

Algebraic Geometry

19 pages; AMSTeX The current, revised and enlarged version features some corrections, more detailed proofs and further applica

Scientific paper

We consider normal projective n-dimensional varieties X whose anticanonical divisor class -K is ample and where every Weil divisor is a rational multiple of K. The index i is the largest integer such that K/i exists as a Weil divisor. We show (i) if X has log-terminal singularities, and in addition 1-forms on the smooth part of X are holomorphic on a resolution, then (-K)^n =< (max(in,n+1))^n; (ii) if the tangent sheaf of X is semistable, then (-K)^n =<(2n)^n. The proof is based on some elementary but possibly surprising slope estimates on sheaves of differential operators on plurianticanonical sheaves. Unlike previous arguments in the smooth case (Nadel, Campana, Kollar-Miyaoka-Mori), rational curves and rational connectedness are not used.

Affiliated with

Also associated with

No associations

Rating

On semipositivity of sheaves of differential operators and the degree of a unipolar Q-Fano variety 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 On semipositivity of sheaves of differential operators and the degree of a unipolar Q-Fano variety, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On semipositivity of sheaves of differential operators and the degree of a unipolar Q-Fano variety will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-576224