On the syzygies of ample line bundles on fake projective planes

TL;DR

This paper investigates the syzygies of ample line bundles on fake projective planes, providing explicit bounds for their powers to satisfy certain algebraic properties, enhancing understanding of their projective embeddings.

Contribution

It offers new explicit bounds for powers of ample line bundles on fake projective planes to satisfy property $N_p$, advancing knowledge of their syzygies.

Findings

Explicit lower bounds for powers of ample line bundles

Verification of property $N_p$ for various line bundles

Improved understanding of projective embeddings on fake projective planes

Abstract

Our goal is to study the syzygies of the projective embeddings defined by ample line bundles on a fake projective plane S. The syzygies are studied in terms of the property $N_p$. For various kinds of ample line bundles, we give explicit lower bounds for their powers above which the property $N_p$ is satisfied.