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New explicit formulas for Faltings' delta-invariant | | Robert Wilms
; | | Date: |
3 May 2016 | | Abstract: | In this paper we give new explicit formulas for Faltings’ $delta$-invariant
in terms of integrals of theta functions, and we deduce an explicit lower bound
for $delta$ only in terms of the genus and an explicit upper bound for the
Arakelov-Green function in terms of $delta$. Furthermore, we give a canonical
extension of $delta$ and the Zhang-Kawazumi invariant $varphi$ to the moduli
space of indecomposable principally polarised complex abelian varieties. As
applications to Arakelov theory, we obtain bounds for the Arakelov heights of
Weierstra{ss} points and for the Arakelov intersection number of any geometric
point with certain torsion line bundles in terms of the Faltings height.
Moreover, we deduce an improved version of Szpiro’s small points conjecture for
cyclic covers of prime degree and an explicit expression for the Arakelov
self-intersection number $omega^2$, an effective version of the Bogomolov
conjecture and an arithmetic analogue of the Bogomolov-Miyaoka-Yau inequality
for hyperelliptic curves. | | Source: | arXiv, 1605.0847 | | Services: | Forum | Review | PDF | Favorites | |
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