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• W1521967315 abstract "In this paper we prove new explicit formulas for Faltings' $delta$-invariant of an arbitrary hyperelliptic Riemann surface. This has several applications: For example we obtain an explicit lower bound for $delta$ depending only on the genus, and we deduce new explicit bounds for the Arakelov self-intersection number $omega^2$ associated to hyperelliptic curves over number fields. Furthermore, we obtain an improved version of Szpiro's small points conjecture for hyperelliptic curves of genus at least $3$. Our method allows us in addition to establish a generalization of Rosenhain's formula on $theta$-derivatives conjectured by Guardia." @default.
• W1521967315 created "2016-06-24" @default.
• W1521967315 creator A5003240350 @default.
• W1521967315 date "2015-05-18" @default.
• W1521967315 modified "2023-10-11" @default.
• W1521967315 title "On Faltings' Delta-Invariant of Hyperelliptic Riemann Surfaces" @default.
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