Seshadri constants on principally polarized abelian surfaces with real multiplication

Abstract Seshadri constants on abelian surfaces are fully understood in the case of Picard number one. Little is known so far for simple higher number. In this paper we investigate principally polarized with real multiplication. They two and might be considered next natural to studied. The challenge not only determine individual line bundles, but understand whole function these surfaces. Our results show one hand that surprisingly complex: multiplication $$\mathbb {Z}[\sqrt{e}]$$ Z [ e ] it consists linear segments never adjacent each other—it behaves like Cantor function. On other hand, prove invariant under an infinite group automorphisms, which shows does have interesting regular behavior globally.