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Multiplicity estimates, interpolation, and transcendence theory. (English) Zbl 1268.11097
Goldfeld, Dorian (ed.) et al., Number theory, analysis and geometry. In memory of Serge Lang. Berlin: Springer (ISBN 978-1-4614-1259-5/hbk; 978-1-4614-1260-1/ebook). 475-498 (2012).
The author discusses the connection between the problems of interpolation and multiplicity estimates in two distinct settings, presented in the common framework of compactifications of commutative algebraic groups. In the former, the multiplicity is imposed at a single very general point of a smooth projective variety, while in the latter the conditions are imposed on an asymptotically growing set of points of the group. Some conjectures and new results are given in both cases.
For the entire collection see [Zbl 1230.00036].

MSC:
11J81 Transcendence (general theory)
14C20 Divisors, linear systems, invertible sheaves
14L40 Other algebraic groups (geometric aspects)
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