Omega-admissible theory II. Deligne pairings over moduli spaces of punctured Riemann surfaces

In Part I, Deligne-Riemann-Roch isometry is generalized for punctured Riema nn surfaces equipped with quasi-hyperbolic metrics. This is achieved by pro ving the Mean Value Lemmas, which explicitly explain how metrized Deligne p airings for omega -admissible metrized line bundles depend on omega. In Par t II, we first introduce several line bundles over Knudsen-Deligne-Mumford compactification of the moduli space (or rather the algebraic stack) of sta ble N-pointed algebraic curves of genus g, which are rather natural and inc lude Weil-Petersson, Takhtajan-Zograf and logarithmic Mumford line bundles. Then we use Deligne-Riemann-Roch isomorphism and its metrized version (pro ved in Part T) to establish some fundamental relations among these line bun dles. Finally, we compute first Chern forms of the metrized Weil-Petersson, Takhtajan-Zograf and logarithmic Mumford line bundles by using results of Wolpert and Takhtajan-Zograf, and show that the so-called Takhtajan-Zograf metric on the moduli space is algebraic.