Multiplicity lemmas and intersections
type: Item
instance of: scholarly article
title: Multiplicity lemmas and intersections
zbMATH Open document ID: 0856.11028
DOI: 10.1007/BF02566006
author: Laurent Denis
published in: Commentarii Mathematici Helvetici
publication date: 1995-10-22T00:00:00Z
full work available at URL: https://eudml.org/doc/140367
review text: This paper studies one of the postulation problems encountered in transcendence theory, where the ambient variety is a smooth compactification \(X\) of a complex commutative algebraic group \(G\), and the zero-dimensional subscheme \(Y\) is the orbit under a finite set of translations of the origin of \(G\), thickened along a subspace of \(\text{Lie} (G)\). The author gets rid of an unnatural constant which occurred in the fundamental upper bound obtained by \textit{P. Philippon} [Bull. Soc. Math. Fr. 114, 355-383 (1986; Zbl 0617.14001)] for the minimal degree of the effective divisors on \(G\) containing \(Y\). The new point in the proof is the appeal to intersection theory, combined with an explicit description of \(\text{Pic} (X)\), and standard properties of Cohen-Macaulay schemes. Remarks: Another type of improvement of the constants in his upper bound has recently been obtained by \textit{P. Philippon} [Rocky Mt. J. Math. 26, 1069-1088 (1996)] while another approach to multiplicity estimates, still based on intersection theory, is given by \textit{M. Nakamaye} [Bull. Soc. Math. Fr. 123, No. 2, 155-188 (1995; Zbl 0841.11037)].
Mathematics Subject Classification ID: 11G10
Mathematics Subject Classification ID: 14C17
zbMATH DE Number: 790580
zbMATH Keywords: group schemes
zbMATH Keywords: zero estimates
zbMATH Keywords: abelian varieties
zbMATH Keywords: multiplicity estimates
zbMATH Keywords: postulation problems
zbMATH Keywords: transcendence theory
zbMATH Keywords: intersection theory
reviewed by: Daniel Bertrand
MaRDI profile type: Publication
OpenAlex ID: W374936599
description: scientific article; zbMATH DE number 790580