Seshadri Constants, Diophantine Approximation, and Roth’s Theorem for Arbitrary Varieties
نویسنده
چکیده
In this paper, we associate an invariant αx(L) to an algebraic point x on an algebraic variety X with an ample line bundle L. The invariant α measures how well x can be approximated by rational points on X , with respect to the height function associated to L. We show that this invariant is closely related to the Seshadri constant ǫx(L) measuring local positivity of L at x, and in particular that Roth’s theorem on P generalizes as an inequality between these two invariants valid for arbitrary projective varieties.
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