Mathematische Zeitschrift

, Volume 284, Issue 3–4, pp 683–714

Loci of curves with subcanonical points in low genus

Article

DOI: 10.1007/s00209-016-1670-5

Cite this article as:
Chen, D. & Tarasca, N. Math. Z. (2016) 284: 683. doi:10.1007/s00209-016-1670-5
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Abstract

Inside the moduli space of curves of genus three with one marked point, we consider the locus of hyperelliptic curves with a marked Weierstrass point, and the locus of non-hyperelliptic curves with a marked hyperflex. These loci have codimension two. We compute the classes of their closures in the moduli space of stable curves of genus three with one marked point. Similarly, we compute the class of the closure of the locus of curves of genus four with an even theta characteristic vanishing with order three at a certain point. These loci naturally arise in the study of minimal dimensional strata of Abelian differentials.

Keywords

Higher Weierstrass points Spin curves Minimal strata of Abelian differentials Effective cycles in moduli spaces of curves 

Mathematics Subject Classification

Primary 14H99 Secondary 14C99 

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of MathematicsBoston CollegeChestnut HillUSA
  2. 2.Department of MathematicsUniversity of UtahSalt Lake CityUSA

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