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Effective divisors on \({\overline{\mathcal{M}}_g}\) associated to curves with exceptional secant planes

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This article is a sequel to Cotterill (Math Zeit 267(3):549–582, 2011), 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 \({\overline{\mathcal{M}}_g}\) 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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  1. Laboratoire de Mathématiques Jean Leray, Unité mixte de recherche 6629 du CNRS, Université de Nantes, 2 rue de la Houssinière, BP 92208, 44322, Nantes Cedex 3, France

    Ethan Cotterill

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  1. Ethan Cotterill
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Correspondence to Ethan Cotterill.

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Cotterill, E. Effective divisors on \({\overline{\mathcal{M}}_g}\) associated to curves with exceptional secant planes. manuscripta math. 138, 171–202 (2012). https://doi.org/10.1007/s00229-011-0491-4

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  • DOI: https://doi.org/10.1007/s00229-011-0491-4

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