Non-Archimedean analytic curves in the complements of hypersurface divisors

Ta Thi Hoai An; J. T. -Y. Wang; P. -M. Wong

paper

Non-Archimedean analytic curves in the complements of hypersurface divisors

arXiv:2004.10625

Abstract

We 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 $P^{n} ∖ \cup_{i = 1}^{n} D_{i}$ where $D_{i}, 1 \leq i \leq n$ , 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 $P^{2} ∖ \cup_{i = 1}^{2} D_{i}$ when $D_{1}, D_{2}$ are generic plane curves with deg $D_{1} +$ deg $D_{2} \geq 4$ .