Positive sheaves of differentials coming from coarse moduli spaces

Details Positive sheaves of differentials coming from coarse moduli spaces Positive sheaves of differentials coming from coarse moduli spaces

2009-04-16

arxiv.org/abs/0904.2445v1

Mathematics

Algebraic Geometry

Scientific paper

Consider a smooth projective family of canonically polarized complex manifolds over a smooth quasi-projective complex base U, and suppose the family is non-isotrivial. If Y is a smooth compactification of U, such that D := Y U is a simple normal crossing divisor, then we can consider the sheaf of differentials with logarithmic poles along D. Viehweg and Zuo have shown that for some number m>0, the m-th symmetric power of this sheaf admits many sections. More precisely, the m-th symmetric power contains an invertible sheaf whose Kodaira-Iitaka dimension is at least the variation of the family. We refine this result and show that this "Viehweg-Zuo sheaf" comes from the coarse moduli space associated to the given family, at least generically. As an immediate corollary, if U is a surface, we see that the non-isotriviality assumption implies that U cannot be special in the sense of Campana.

Affiliated with

Also associated with

No associations

Rating

Positive sheaves of differentials coming from coarse moduli spaces 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 Positive sheaves of differentials coming from coarse moduli spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Positive sheaves of differentials coming from coarse moduli spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-464660