Signature divisor on the moduli of curves, signature defect and its applications

我们将退化曲线的纤维芽的局部特征表示为“模项”和“单项”之和。前者定义为稳定曲线的模空间上的特征因子的模映射的拉回(与吉川仁一共同工作)。后者称为局部特征亏损，它是通过将拓扑单项数据解释为对稳定约化的群作用而得到的。

We have a new formulation of the local signature of a fiber germ of degeneration of curves as a sum of "moduli term" and "monodromy term" in the following sense.The former is defined as the pull back by the moduli map of the signature divisor on the moduli space of stable curves(joint work with Ren-ichi Yoshikawa).The latter is called local signature defect, which is obtained via the orbifold signature theorem by interpreting the topological monodromy data as a group action to the stable reduction.