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Ferretti, Roberto G.

Diophantine approximations and toric deformations. (English) Zbl 1087.11047

Duke Math. J. 118, No. 3, 493-522 (2003).
Some time ago the reviewer and G. Wüstholz applied the (then new) product theorem in Diophantine approximation to subvarieties of projective spaces, and obtained a new proof of Schmidt’s theorem (on linear forms). The exponents in these result where governed by invariants of filtered vector-spaces.
The paper under review gives a systematic treatment of these invariants for subvarieties of projective spaces, mainly in terms of their Chow-forms. At the end the author gives many examples of the results which can be achieved by this method.
Reviewer: Gerd Faltings (Bonn)

Cited in 2 Documents

MSC:

11J25 Diophantine inequalities
11J95 Results involving abelian varieties
14G40 Arithmetic varieties and schemes; Arakelov theory; heights
14M25 Toric varieties, Newton polyhedra, Okounkov bodies

Keywords:

Diophantine approximation; Chow-forms
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\textit{R. G. Ferretti}, Duke Math. J. 118, No. 3, 493--522 (2003; Zbl 1087.11047)
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