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• W2949661646 abstract "We formulate, and in some cases prove, three statements concerning the purity or, more generally the naturality of the resolution of various rings one can attach to a generic curve of genus g and a torsion point of order l in its Jacobian. These statements can be viewed an analogues of Green's Conjecture and we verify them computationally for bounded genus. We then compute the cohomology class of the corresponding non-vanishing locus in the moduli space R_{g,l} of twisted level l curves of genus g and use this to derive results about the birational geometry of R_{g, l}. For instance, we prove that R_{g,3} is a variety of general type when g>11 and the Kodaira dimension of R_{11,3} is greater than or equal to 19. In the last section we explain probabilistically the unexpected failure of the Prym-Green conjecture in genus 8 and level 2." @default.
• W2949661646 created "2019-06-27" @default.
• W2949661646 creator A5090361004 @default.
• W2949661646 date "2012-08-16" @default.
• W2949661646 modified "2023-09-27" @default.
• W2949661646 title "Syzygies of torsion bundles and the geometry of the level l modular variety over Mg" @default.
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• W2949661646 doi "https://doi.org/10.14288/1.0043247" @default.
• W2949661646 hasPublicationYear "2012" @default.
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