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- W1605400273 abstract "Let G be a commutative algebraic group embedded in projective space and $$Gamma $$ a finitely generated subgroup of G. From these data we construct a chain of algebraic subgroups of G which is intimately related to obstructions to multiplicity or interpolation estimates used in transcendental number theory and algebraic independence. Let $$gamma _1,ldots ,gamma _l$$ denote a family of generators of $$Gamma $$ and, for any $$S>1$$ , let $$Gamma (S)$$ be the set of elements $$n_1gamma _1+cdots +n_lgamma _l$$ with integers $$n_j$$ such that $$|n_j| < S$$ . Then this chain of subgroups controls, for large values of S, the distribution of $$Gamma (S)$$ with respect to algebraic subgroups of G. As an application we essentially determine (up to multiplicative constants) the locus of common zeros of all $$P in H^0(overline{G} ,mathcal{O}(D))$$ which vanish to at least some given order at all points of $$Gamma (S)$$ . When D is very small this result reduces to a multiplicity estimate; when D is very large it is a kind of interpolation estimate." @default.
- W1605400273 created "2016-06-24" @default.
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- W1605400273 date "2015-08-13" @default.
- W1605400273 modified "2023-10-15" @default.
- W1605400273 title "Connecting interpolation and multiplicity estimates in commutative algebraic groups" @default.
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- W1605400273 doi "https://doi.org/10.1007/s00208-015-1273-1" @default.
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