Components of moduli spaces of spin curves with the expected codimension

الأصل · EN

We prove a conjecture of Gavril Farkas claiming that for all integers r ≥ 2 and g ≥ r+22 there exists a component of the locus Sʳg of spin curves with a theta characteristic L such that h⁰(L) ≥ r+1 and h⁰(L)≡ r+1 (mod 2) which has codimension r+12 inside the moduli space Sg of spin curves of genus g.