In this talk, by using Seshadri constants for subschemes, we establish a second main theorem of Nevanlinna theory for holomorphic curves intersecting closed subschemes in (weak) subgeneral position. As an application of our second main theorem, we obtain a Brody hyperbolicity result for the complement of nef effective divisors. We also give the corresponding Schmidt's subspace theorem and arithmetic hyperbolicity result in Diophantine approximation.

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