Moduli of theta-characteristics via Nikulin surfaces
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We study moduli spaces of K3 surfaces endowed with a Nikulin involution and their image in the moduli space Rg 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 Rg is a section of a Nikulin surface if and only if g ≤ 7 and g ≠ 6. Furthermore, R7 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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/810ff7934cb20c6c9d02fe08b0e43f62154fd242
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- The geometry of the moduli space of odd spin curves (2010, result): “and 0.1 coupled with results from [F3], show that for 9 ≤g ≤11, the space S− g is uniruled while S + g is of general type! Finally, we notethat S − 8 is unirational whereas S+ 8 is of Calabi-Yau type [FV]. We describe the main steps in the proof of Theorem 0.4. First, we use that for all g ≥4 and ℓ ”