Here we investigate some birational properties of two collections of moduli spaces, namely moduli spaces of (pointed) stable curves and of (pointed) spin curves. In particular, we focus on vanishings of Hodge numbers of type (p,0) and on computations of the Kodaira dimension. Our methods are purely algebro-geometric and rely on an induction argument on the number of the points and the genus of the curves.
Moduli of curves and spin structures via algebraic geometry / G. Bini, C. Fontanari. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 358:7(2006), pp. 3207-3217. [10.1090/S0002-9947-06-03838-4]
Moduli of curves and spin structures via algebraic geometry
G. BiniPrimo
;
2006
Abstract
Here we investigate some birational properties of two collections of moduli spaces, namely moduli spaces of (pointed) stable curves and of (pointed) spin curves. In particular, we focus on vanishings of Hodge numbers of type (p,0) and on computations of the Kodaira dimension. Our methods are purely algebro-geometric and rely on an induction argument on the number of the points and the genus of the curves.
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