Components with the expected codimension in the moduli scheme of stable spin curves

Edoardo Ballico


Here we study the Brill–Noether theory of “extremal” Cornalba’s theta-characteristics on stable curves C of genus g, where “extremal” means that they are line bundles on a quasi-stable model of C with #(Sing(C)) exceptional components.


Stable curve; theta-characteristic; spin curve; Brill–Noether theory

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Arbarello, E., Cornalba, M., Griffiths, P. A., Geometry of Algebraic Curves. Vol. II, Springer, Berlin, 2011.

Ballico, E., Sections of theta-characteristics on stable curves, Int. J. Pure Appl. Math. 54, No. 3 (2009), 335–340.

Benzo, L., Components of moduli spaces of spin curves with the expected codimension, Mathematische Annalen (2015), DOI 10.1007/s00208-015-1171-6, arXiv:1307.6954.

Caporaso, L., A compactification of the universal Picard variety over the moduli space of stable curves, J. Amer. Math. Soc. 7, No. 3 (1994), 589–660.

Cornalba, M., Moduli of curves and theta-characteristics. Lectures on Riemann surfaces (Trieste, 1987), World Sci. Publ., Teaneck, NJ, 1989, 560–589.

Farkas, G., Gaussian maps, Gieseker–Petri loci and large theta-characteristics, J. Reine Angew. Math. 581 (2005), 151–173.

Fontanari, C., On the geometry of moduli of curves and line bundles, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 16, No. 1 (2005), 45–59.

Harris, J., Theta-characteristics on algebraic curves, Trans. Amer. Math. Soc. 271 (1982), 611–638.

Jarvis, T. J., Torsion-free sheaves and moduli of generalized spin curves, Compositio Math. 110, No. 3 (1998), 291–333.

Data publikacji: 2015-11-30 09:21:10
Data złożenia artykułu: 2015-09-03 12:01:48


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