Seshadri constants, diophantine approximation, and Roth's theorem for arbitrary varieties

In this paper, we associate an invariant to an algebraic point on an algebraic variety with an ample line bundle . The invariant measures how well can be approximated by rational points on , with respect to the height function associated to . We show that this invariant is closely related to the Seshadri constant measuring local positivity of at , and in particular that Roth's theorem on generalizes as an inequality between these two invariants valid for arbitrary projective varieties.