Gaussian Maps, Gieseker-petri Loci and Large Theta-characteristics
نویسنده
چکیده
For an integer g ≥ 1 we consider the moduli space Sg of smooth spin curves parametrizing pairs (C,L), where C is a smooth curve of genus g and L is a thetacharacteristic, that is, a line bundle on C such that L2 ∼= KC . It has been known classically that the natural map π : Sg → Mg is finite of degree 2 2g and that Sg is a disjoint union of two components Seven g and S odd g corresponding to even and odd theta-characteristics. A geometrically meaningful compactification Sg of Sg has been constructed by Cornalba by means of stable spin curves of genus g (cf. [C]). The space Sg and more generally the
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