Families of translations of commutative algebraic groups. (English) Zbl 0657.14026

Abstract: It is shown that for certain compactifications of a connected commutative algebraic group G in \({\mathbb{P}}_ N\) the translation by points g of G can be described completely by quadratic forms in such a way, that the forms depend holomorphically on g. This implies that some zero estimates in transcendence theory are effective.
Reviewer: D.M.Snow


14L30 Group actions on varieties or schemes (quotients)
11J81 Transcendence (general theory)
Full Text: DOI


[1] Bertrand, D., Lemmes de zéros et nombres transcendants, (Sém. Bourbaki (1985-1986)), n ∘ 652 · Zbl 0613.14001
[2] Knop, F.; Lange, H., Commutative algebraic groups and intersection of quadrics, Math. Ann., 267, 555-571 (1984) · Zbl 0544.14028
[3] Knop, F.; Lange, H., Some remarks on compactifications of commutative algebraic groups, Comm. Helv., 60, 497-507 (1985) · Zbl 0587.14030
[4] Lange, H., Translations sur les groupes algébriques commutatifs, C.R. Acad. Sci. Paris, 300, 255-258 (1985) · Zbl 0579.14040
[5] Lange, H.; Ruppert, W., Complete systems of addition laws on abelian varieties, Invent. Math., 79, 603-610 (1985) · Zbl 0577.14035
[6] Mumford, D., Abelian Varieties (1970), Oxford Univ. Press: Oxford Univ. Press London · Zbl 0198.25801
[7] Philippon, P., Lemmes de zéros dans les groupes algébriques commutatifs, Bull. Soc. Math. France, 114, 355-383 (1986) · Zbl 0617.14001
[8] Wüstholz, G., Multiplicity Estimates on Group Varieties (1984), Max Planck Inst: Max Planck Inst Bonn · Zbl 0675.10024
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