On the canonical degrees of curves in varieties of general type

Details On the canonical degrees of curves in varieties of general type On the canonical degrees of curves in varieties of general type

2010-03-19

arxiv.org/abs/1003.3804v2

Mathematics

Algebraic Geometry

14 pages

Scientific paper

A widely believed conjecture predicts that curves of bounded geometric genus lying on a variety of general type form a bounded family. One may even ask whether the canonical degree of a curve $C$ in a variety of general type is bounded from above by some expression $a\chi(C)+b$, where $a$ and $b$ are positive constants, with the possible exceptions corresponding to curves lying in a strict closed subset (depending on $a$ and $b$). A theorem of Miyaoka proves this for smooth curves in minimal surfaces, with $a>3/2$. A conjecture of Vojta claims in essence that any constant $a>1$ is possible provided one restricts oneself to curves of bounded gonality. We show by explicit examples coming from the theory of Shimura varieties that in general, the constant $a$ has to be at least equal to the dimension of the ambient variety. We also prove the desired inequality in the case of compact Shimura varieties.

Affiliated with

Also associated with

No associations

Rating

On the canonical degrees of curves in varieties of general type 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 the canonical degrees of curves in varieties of general type, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the canonical degrees of curves in varieties of general type will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-354661