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References
S. Y. Arakelov, An intersection theory for divisors on an arithmetic surface, Izv. Akad. Nauk., 38 (1974), 1179–1192; cf. Math. USSR Izv., 8 (1974), 1167–1180.
H. F. Baker, On the hyperelliptic sigma functions, Amer. J. Math., 20 (1898), 301–384.
J.-B. Bost, Fonctions de Green-Arakelov, fonctions thêta et courbes de genre 2, C. R. Acad. Sci. Paris Ser. I, 305 (1987), 643–646.
V. M. Buchstaber, V. Z. Enolskii, and D. V. Leykin, Kleinian functions, hyperelliptic jacobians and applications, Rev. Math. Math. Phys., 10 (1997), 1–125.
V. M. Buchstaber, V. Z. Enolskii, and D.V. Leykin, Rational analogs of abelian functions, Functional Anal. Appl., 33-2 (1999), 83–94.
V. M. Buchstaber, D. V. Leykin, and V. Z. Enolskii, σ-functions of (n, s)-curves, Russian Math. Surveys, 54 (1999), 628–629.
G. Faltings, Calculus on arithmetic surfaces, Ann. Math., 119 (1984), 387–424.
W. Fulton and J. Harris, Representation Theory: A First Course, Graduate Texts in Mathematics 129, Springer-Verlag, New York, 1991.
D. Grant, A generalization of Jacobi’s derivative formula to dimension two, J. Reine Angew. Math., 392 (1988), 125–136.
R. de Jong, Arakelov invariants of Riemann surfaces, preprint, submitted.
R. de Jong, Explicit Mumford Isomorphism for Hyperelliptic Curves, Prépublication M/04/51, Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France, 2004; submitted.
Y. Ônishi, Determinant expressions for hyperelliptic functions (with an appendix by Shigeki Matsutani), preprint.
P. Lockhart, On the discriminant of a hyperelliptic curve, Trans. Amer. Math. Soc., 342-2 (1994), 729–752.
D. Mumford, Tata Lectures on Theta I, II, Progress in Mathematics 28, 43, Birkhäuser Boston, Cambridge, MA, 1984.
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de Jong, R. (2005). Faltings’ Delta-Invariant of a Hyperelliptic Riemann Surface. In: van der Geer, G., Moonen, B., Schoof, R. (eds) Number Fields and Function Fields—Two Parallel Worlds. Progress in Mathematics, vol 239. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4447-4_10
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