超曲面因子补空间中的非阿基米德解析曲线
Non-Archimedean analytic curves in the complements of hypersurface divisors
摘要：
研究了非阿基米德解析映射到光滑射影簇的超曲面因子补的退化维数。我们还证明了不存在到$P^n\setminus\cup_{i= 1}^n D_i$的非阿基米德解析映射，其中$D_i, 1\le i\le n$，是在一般位置上至少2次且横截相交的超曲面。证明了当$D_1, D_2$是一般平面曲线且度$D_1+$度为$D_2\ge 4$时，不存在到$P^2\setminus\cup_{i=1}^2 D_i$的非阿基米德解析映射.
英文摘要：
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 $P^n\setminus\cup_{i= 1}^n D_i$ where $D_i, 1\le i\le n$, 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 $P^2\setminus\cup_{i=1}^2 D_i$ when $D_1, D_2$ are generic plane curves with deg$D_1+$deg$D_2\ge 4$.
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