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摘要
Harris and Morrison (Invent. Math. 99:321-355, 1990, Theorem 2.5), constructed certain semistable fibrations in -gonal curves of genus , such that for every the corresponding modular curves give a sweeping family in the -gonal locus . Their construction depends on the choice of a smooth curve . We show that if the genus is sufficiently high with respect to , then the ratio is asymptotically with respect to . Moreover, if the conjectured estimates given in Harris and Morrison (Invent. Math. 99:321-355, 1990, pp. 351-352) hold, we show that if is big enough, then is a surface of positive index.
- 出版日期2015-5
