Linear sections of the Severi variety and moduli of curves

Details Linear sections of the Severi variety and moduli of curves Linear sections of the Severi variety and moduli of curves

2007-10-08

arxiv.org/abs/0710.1623v1

Mathematics

Algebraic Geometry

28 pages, 4 figures

Scientific paper

We study the Severi variety $V_{d,g}$ of plane curves of degree $d$ and geometric genus $g$. Corresponding to every such variety, there is a one-parameter family of genus $g$ stable curves whose numerical invariants we compute. Building on the work of Caporaso and Harris, we derive a recursive formula for the degrees of the Hodge bundle on the families in question. For $d$ large enough, these families induce moving curves in $\bar{M}_g$. We use this to derive lower bounds for the slopes of effective divisors on $\bar{M}_g$. Another application of our results is to various enumerative problems on $V_{d,g}$.

Affiliated with

Also associated with

No associations

Rating

Linear sections of the Severi variety and moduli of curves 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 Linear sections of the Severi variety and moduli of curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Linear sections of the Severi variety and moduli of curves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-544696