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Mathematische Annalen

, Volume 354, Issue 2, pp 465–496 | Cite as

Moduli of theta-characteristics via Nikulin surfaces

  • Gavril FarkasEmail author
  • Alessandro Verra
Article

Abstract

We study moduli spaces of K3 surfaces endowed with a Nikulin involution and their image in the moduli space R g of Prym curves of genus g. We observe a striking analogy with Mukai’s well-known work on ordinary K3 surfaces. Many of Mukai’s results have a very precise Prym-Nikulin analogue, for instance a general Prym curve from R g is a section of a Nikulin surface if and only if g ≤ 7 and g ≠ 6. Furthermore, R 7 has the structure of a fibre space over the corresponding moduli space of polarized Nikulin surfaces. We then use these results to study the geometry of the moduli space \({S_g^+}\) of even spin curves, with special emphasis on the transition case of \({S_8^+}\) which is a 21-dimensional Calabi-Yau variety.

Keywords

Modulus Space Double Cover Exceptional Divisor Spin Curve Effective Divisor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Institut Für Mathematik, Humboldt-Universität zu BerlinBerlinGermany
  2. 2.Dipartimento di MatematicaUniversitá Roma TreRomeItaly

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