Mathematics – Algebraic Geometry
Scientific paper
2010-04-02
Mathematics
Algebraic Geometry
An expansion of the second part of arXiv:0706.2049. New material includes a discussion of how Le Barz's cycle-theoretic secant
Scientific paper
This paper is a sequel to \cite{C}, in which the author studies secant planes to linear series on a curve that is general in moduli. In that paper, the author proves that a general curve has no linear series with exceptional secant planes, in a very precise sense. Consequently, it makes sense to study effective divisors on $\ov{\mc{M}}_g$ associated to curves equipped with secant-exceptional linear series. Here we describe a strategy for computing the classes of those divisors. We pay special attention to the extremal case of $(2d-1)$-dimensional series with $d$-secant $(d-2)$-planes, which appears in the study of Hilbert schemes of points on surfaces. In that case, modulo a combinatorial conjecture, we obtain hypergeometric expressions for tautological coefficients that enable us to deduce the asymptotics in $d$ of our divisors' virtual slopes.
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