The Toledo invariant, and Seshadri constants of fake projective planes

TL;DR

This paper explicitly computes Seshadri constants for all ample line bundles on fake projective planes using the Toledo invariant, linking complex hyperbolic geometry with algebraic geometry.

Contribution

It provides the first explicit calculations of Seshadri constants on fake projective planes, utilizing the Toledo invariant to characterize certain curves.

Findings

Explicit Seshadri constants for all ample line bundles on fake projective planes

Connection established between Toledo invariant and algebraic geometry of fake projective planes

Characterization of $ ext{C}$-Fuchsian curves in complex hyperbolic spaces

Abstract

The purpose of this paper is to explicitly compute the Seshadri constants of all ample line bundles on fake projective planes. The proof relies on the theory of the Toledo invariant, and more precisely on its characterization of $\C$-Fuchsian curves in complex hyperbolic spaces.