This paper finds estimates for the slope of the moduli space of curves of (small) genus g = 10, 12, 13, 14 and for the moduli space of abelian varieties of dimension five. Assume that one can find a surface S fibered over a rational curve such that the fibers are generic curves of genus g. Then one can find an estimate of the slope of Mg in terms of some invariants of S. This paper uses this idea by constructing for each of the given genera a surface containing a generic curve. For abelian varieties of genus five, the authors use that the Prym map R6 !A5 is dominant and construct again surfaces involved in the curves of the double covering corresponding to the Prym point.
Bruno, A., Fontanari, C., Verra, A. (2008). Geometry of effective divisors on moduli spaces. In Vector bundles and low codimensional subvarieties: state of the art and recent developments (pp. 1-12). ROMA : Aracne Editrice.
Geometry of effective divisors on moduli spaces
BRUNO, Andrea;VERRA, Alessandro
2008-01-01
Abstract
This paper finds estimates for the slope of the moduli space of curves of (small) genus g = 10, 12, 13, 14 and for the moduli space of abelian varieties of dimension five. Assume that one can find a surface S fibered over a rational curve such that the fibers are generic curves of genus g. Then one can find an estimate of the slope of Mg in terms of some invariants of S. This paper uses this idea by constructing for each of the given genera a surface containing a generic curve. For abelian varieties of genus five, the authors use that the Prym map R6 !A5 is dominant and construct again surfaces involved in the curves of the double covering corresponding to the Prym point.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
