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Analytic invariants in Arakelov theory for curves

✍ Scribed by Jordi Guàrdia

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
320 KB
Volume
329
Category
Article
ISSN
0764-4442

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✦ Synopsis

Arakelov theory for Riemann surfaces is based on two analytic invariants: the Green function and Faltings 6 invariant. Both invariants are hard to compute and they are only known in a few cases (cJ: [3], [l]). They are related by a formula of Faltings, which also involves the theta-function on the Jacobian of the curve. In any case, it is an ineffective relation, because three of the four terms involved cannot be computed in general. We introduce a function \jJll on the Jacobian of the curve, which gives a new relation between the Green function and the Faltings 6 invariant. Our ]]Jjl function is easily computable because it is defined in terms of derivatives of the theta-function. 0 Academic des SciencesMsevier, Paris

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