Sharp degree bounds for fake weighted projective spaces

TL;DR

This paper establishes precise upper limits on the anticanonical degree of fake weighted projective spaces, based solely on their dimension and Gorenstein index, advancing understanding of their geometric properties.

Contribution

It provides the first sharp bounds on the anticanonical degree for fake weighted projective spaces depending only on key invariants.

Findings

Sharp upper bounds depend only on dimension and Gorenstein index.

Results improve previous bounds and clarify the structure of fake weighted projective spaces.

The bounds are optimal and applicable to classification problems.

Abstract

We give sharp upper bounds on the anticanonical degree of fake weighted projective spaces, only depending on the dimension and the Gorenstein index.