论文标题
seshadri常数在主要乘法的主要两极分化的阿贝尔表面
Seshadri constants on principally polarized abelian surfaces with real multiplication
论文作者
论文摘要
在Picard第一的情况下，Abelian表面上的Seshadri常数已完全理解。到目前为止，对于更高的PICARD编号的简单Abelian表面而言，鲜为人知。在本文中，我们研究了主要乘法的主要极化的阿贝尔表面。它们是PICARD的第二名，可能被认为是下一个要研究的自然案例。面临的挑战不仅要确定单个线束的seshadri常数，而且要在这些表面上了解整个\ emph {seshadri函数}。一方面，我们的结果表明，此功能令人惊讶地复杂：在$ \ mathbb z [\ sqrt e] $中具有真实乘法的表面上，它由从未彼此相邻的线性段组成 - 它的行为与cantor函数一样。另一方面，我们证明了seshadri函数在无限的自动形态下是不变的，这表明它在全球范围内确实具有有趣的常规行为。
Seshadri constants on abelian surfaces are fully understood in the case of Picard number one. Little is known so far for simple abelian surfaces of higher Picard number. In this paper we investigate principally polarized abelian surfaces with real multiplication. They are of Picard number two and might be considered the next natural case to be studied. The challenge is to not only determine the Seshadri constants of individual line bundles, but to understand the whole \emph{Seshadri function} on these surfaces. Our results show on the one hand that this function is surprisingly complex: On surfaces with real multiplication in $\mathbb Z[\sqrt e]$ it consists of linear segments that are never adjacent to each other -- it behaves like the Cantor function. On the other hand, we prove that the Seshadri function it is invariant under an infinite group of automorphisms, which shows that it does have interesting regular behavior globally.
