Integral points, divisibility between values of polynomials and entire curves on surfaces |
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Authors: | Pietro Corvaja Umberto Zannier |
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Institution: | a Dip. di Matematica e Informatica, Via delle Scienze, 33100 Udine, Italy b Scuola Normale Superiore, Piazza dei Cavalieri, 7, 56100 Pisa, Italy |
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Abstract: | We prove some new degeneracy results for integral points and entire curves on surfaces; in particular, we provide the first examples, to our knowledge, of a simply connected smooth variety whose sets of integral points are never Zariski-dense. Some of our results are connected with divisibility problems, i.e. the problem of describing the integral points in the plane where the values of some given polynomials in two variables divide the values of other given polynomials. |
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Keywords: | Integral points Vojta's conjecture Subspace Theorem |
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