Gaussian maps, Gieseker-Petri loci and large theta-characteristics

Details Gaussian maps, Gieseker-Petri loci and large theta-characteristics Gaussian maps, Gieseker-Petri loci and large theta-characteristics

2004-02-03

arxiv.org/abs/math/0402042v2

J. reine angew. Math. 581(2005), 151-173.

Mathematics

Algebraic Geometry

22 pages. Minor revisions, to appear in Crelle

Scientific paper

We analyze the stratification of the moduli space S_g of spin curves of genus g given by the dimension of the theta-characteristic. Using the relation between gaussian maps and the strata S_g^r, we construct "regular" components of S_g^r having expected codimension r(r+1)/2 inside S_g. We also relate moduli spaces of pointed curves with a moving spin structure to the classical Gieseker-Petri loci in M_g. We show that the locus of curves for which the Gieseker-Petri theorem fails for a pencil is always a divisor on M_g. Finally, we give a sufficient criterion for the injectivity of Gaussian maps of arbitrary line bundles on general curves of genus g.

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