The birational type of the moduli space of even spin curves
Gavril Farkas
TL;DR
This paper determines the Kodaira dimension of the moduli space of even spin curves across all genera, revealing it is of negative, non-negative, or general type depending on the genus, with one potential exception.
Contribution
It provides a comprehensive classification of the Kodaira dimension of the moduli space of even spin curves for all genera, filling a significant gap in algebraic geometry.
Findings
Negative Kodaira dimension for g<8
Non-negative Kodaira dimension at g=8
General type for g>8
Abstract
We determine the Kodaira dimension of the moduli space of even spin curves for all genera, with one possible exception: The scheme S_g has negative Kodaira dimension for g<8 and it is of general type for g>8. The Kodaira dimension of S_8 is non-negative.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometry and complex manifolds