Maximal Rank Divisors on M_g,n

2017/05/11 by İrfan Kadıköylü, Kadıköylü, İrfan
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1705.04250

arxiv created 2018/03/24 · arxiv updated 2018/03/28

Abstract

We compute the class of the effective divisors on M_g,n, which are set theoretically equal to the locus of moduli points [C,p₁,… ,p_n] where C lies on a quadric under the map given by the linear series |K_C-p₁-… -p_n|. Using this divisor class we show that the moduli spaces M_16,8 and M_17,8 are of general type. We also note that the divisor classes computed in the papers \citeFV1 and \citeFV2 can be used to show that M_12,10 is of general type as well.

Related

• Extremal divisors on moduli spaces of rational curves with marked points
• Effective divisors in M_g,n from abelian differentials
• An Effective Divisor in M_g Defined by Ramification Conditions
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• Effective divisors on moduli spaces of curves and abelian varieties