The geometry of the moduli space of odd spin curves
78 citations recorded by the source corpus.
The spin moduli spaceSg is the parameter space of theta characteristics (spin structures) on stable curves of genus g. It has two connected components, S g andS + g , depending on the parity of the spin structure. We establish a complete birational classication by Kodaira dimension of the odd componentS g of the spin moduli space. We show thatS g is uniruled for g < 12 and even unirational for g 8. In this range, introducing the concept of cluster for the Mukai variety whose one-dimensional linear sections are general canonical curves of genus g, we construct new birational models ofS g . These we then use to explicitly describe the birational structure of S g . For instance, S 8 is birational to a locally trivial P 7 -bundle over the moduli space of elliptic curves with seven pairs of marked points. For g 12, we prove thatS g is a variety of general type. In genus 12, this requires the construction of a counterexample to the Slope Conjecture on eective divisors on the moduli space of stable curves of genus 12.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/9bfaa1692394ae714e2a2681eaa0c7021cd3559d
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Moduli of theta-characteristics via Nikulin surfaces (2011, background): “h to highlight the following result, see Theorem 0.1: MODULI OF THETA-CHARACTERISTICS VIA NIKULIN SURFACES 5 S+ 8 is a variety of Calabi-Yau type. We observe the curious fact that S− 8 is unirational [FV] whereas S + 8 is not even uniruled. In contrast to the case of S∓ g , the birational classificat”
- The moduli space of multi-scale differentials. (2019, unknown): “the case of the moduli space of curves, this opens the gate towards determining the Kodaira dimension of PΩMg,n(µ). This has been solved so far only for some series of cases, see [Gen18], [Bar18] and [FV14]. THE MODULI SPACE OF MULTI-SCALE DIFFERENTIALS 5 A third large circle of potential applicatio”