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On the gonality of stable curves

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  • Juliana Coelho
  • Frederico Sercio

Abstract

In this paper we use admissible covers to investigate the gonality of a stable curve C over C. If C is irreducible, we compare its gonality to that of its normalization. If C is reducible, we compare its gonality to that of its irreducible components. In both cases we obtain lower and upper bounds. Furthermore, we show that four admissible covers constructed give rise to generically injective maps between Hurwitz schemes. We show that the closures of the images of three of these maps are components of the boundary of the target Hurwitz schemes, and the closure of the image of the remaining map is a component of a certain codimension‐1 subscheme of the boundary of the target Hurwitz scheme.

Suggested Citation

  • Juliana Coelho & Frederico Sercio, 2019. "On the gonality of stable curves," Mathematische Nachrichten, Wiley Blackwell, vol. 292(11), pages 2338-2351, November.
    • Handle: RePEc:bla:mathna:v:292:y:2019:i:11:p:2338-2351
    DOI: 10.1002/mana.201600376
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