Lange, Herbert Families of translations of commutative algebraic groups. (English) Zbl 0657.14026 J. Algebra 109, 260-265 (1987). 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 Cited in 7 Documents MSC: 14L30 Group actions on varieties or schemes (quotients) 11J81 Transcendence (general theory) Keywords:connected commutative algebraic group; translation by points; transcendence theory PDFBibTeX XMLCite \textit{H. Lange}, J. Algebra 109, 260--265 (1987; Zbl 0657.14026) Full Text: DOI References: [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.