论文标题
narasimhan-simha的收敛性riemann表面的退化家族的措施
Convergence of Narasimhan-Simha measures on degenerating families of Riemann surfaces
论文作者
论文摘要
鉴于紧凑的Riemann Surface $ Y $和正整数$ M $，Narasimhan和Simha定义了与$ m $ y $相关的$ y $ - the tensor tensor bundle的量子。我们研究了该度量的极限对黎曼表面的全态家族的限制，并可以半固定。收敛发生在混合空间上，其中央纤维是Amini和Baker的相关Metrized曲线复合物。我们还研究了由Narasimhan-Simha度量定义的Hermitian配对引起的度量的极限。对于$ m = 1 $，这两种措施都与$ y $的伯格曼措施一致。我们还将narasimhan-simha测度的定义扩展到$ \ overline {\ Mathcal {m} _g} $的边界上的单数曲线，以使这些措施形成$ \ overline {\ Mathcal {\ Mathcal {m} _g} $的通用曲线上的连续度量。
Given a compact Riemann surface $Y$ and a positive integer $m$, Narasimhan and Simha defined a measure on $Y$ associated to the $m$-th tensor power of the canonical line bundle. We study the limit of this measure on holomorphic families of Riemann surfaces with semistable reduction. The convergence takes place on a hybrid space whose central fiber is the associated metrized curve complex in the sense of Amini and Baker. We also study the limit of the measure induced by the Hermitian pairing defined by the Narasimhan-Simha measure. For $m = 1$, both these measures coincide with the Bergman measure on $Y$. We also extend the definition of the Narasimhan-Simha measure to the singular curves on the boundary of $\overline{\mathcal{M}_g}$ in such a way that these measures form a continuous family of measures on the universal curve over $\overline{\mathcal{M}_g}$.
