Q-admissible theory II. Deligne pairings over moduli spaces by Weng L.
By Weng L.
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1), we see that up to some universal constant depending only on (g, N ), there exists an isometry (λm , hQ,m ) λm hyp , 280 L. Weng which in particular gives an interpretation of our new determinant metric in terms of the Selberg zeta function. This completes the proof of the Theorem. As a direct consequence, we have the following Corollary. The Takhtajan-Zograf metric on moduli space of punctured Riemann surfaces is algebraic. Fundamental relation IV . With the same notation as above, on Mg,N , for a fixed m ≥ 1, up to some universal constant depending only on g, N , such that there exists canonical isometry (λm , hQ,m )⊗12 ∆WP ⊗6m hyp 2 −6m+1 ⊗ ∆TZ ⊗−1 .
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