Non-archimedean analytic curves in the complements of hypersurface divisors

AbstractWe study the degeneration dimension of non-archimedean analytic maps into the complement of hypersurface divisors of smooth projective varieties. We also show that there exist no non-archimedean analytic maps into Pn∖⋃i=1nDi where Di, 1⩽i⩽n, are hypersurfaces of degree at least 2 in general position and intersecting transversally. Moreover, we prove that there exist no non-archimedean analytic maps into P2∖⋃i=12Di when D1, D2 are generic plane curves with degD1+degD2⩾4