Mathematische Annalen

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

Moduli of theta-characteristics via Nikulin surfaces

  • Gavril FarkasEmail author
  • Alessandro Verra


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.


Modulus Space Double Cover Exceptional Divisor Spin Curve Effective Divisor 
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© 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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