Components of moduli spaces of spin curves with the expected codimension II

2015/02/18 by Benzo, Luca
#14H10 #14H51 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1502.05262

Abstract

We prove that for all integers r ≥ 2 and g ≥ \lfloor (r²+10r+1)/(4) \rfloor there exists a component of the locus S^r_g of spin curves with a theta characteristic L such that h⁰(L) ≥ r+1 and h⁰(L)≡ r+1 (mod 2) which has expected codimension \binomr+12 inside the moduli space S_g of spin curves of genus g.

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• On the geometry of the moduli space of spin curves
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• Enriched spin curves on stable curves with two components
• Szegő kernels and Scorza quartics on the moduli space of spin curves