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This paper is a sequel to \cite{C}, in which the author studies secant planesto linear series on a curve that is general in moduli. In that paper, theauthor proves that a general curve has no linear series with exceptional secantplanes, in a very precise sense. Consequently, it makes sense to studyeffective divisors on $\ov{\mc{M}}_g$ associated to curves equipped withsecant-exceptional linear series. Here we describe a strategy for computing theclasses of those divisors. We pay special attention to the extremal case of$(2d-1)$-dimensional series with $d$-secant $(d-2)$-planes, which appears inthe study of Hilbert schemes of points on surfaces. In that case, modulo acombinatorial conjecture, we obtain hypergeometric expressions for tautologicalcoefficients that enable us to deduce the asymptotics in $d$ of our divisors'virtual slopes.

Effective divisors on $\ov{\mc{M}}_g$ associated to curves with exceptional secant planes