A generalization of the Subspace Theorem with polynomials of higher degree
Jan-Hendrik Evertse, Roberto G. Ferretti
Abstract
Recently, Corvaja and Zannier obtained an extension of the Subspace Theorem with arbitrary homogeneous polynomials of arbitrary degreee instead of linear forms. Their result states that the set of solutions in Pn(K) (K number field) of the inequality being considered is not Zariski dense. In our paper we prove by a different method a generalization of their result, in which the solutions are taken from an arbitrary projective variety X instead of Pn. Further, we give a quantitative version which states in a precise form that the solutions with large height lie ina finite number of proper subvarieties of X, with explicit upper bounds for the number and for the degrees of these subvarieties.
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