A note on the Gromov width of toric manifolds

TL;DR

This paper establishes upper bounds on the Gromov width of toric manifolds using combinatorial invariants, extending known bounds from uniruled projective Kähler manifolds.

Contribution

It applies a general bound on Gromov width to toric varieties, deriving explicit bounds based on combinatorial data.

Findings

Upper bounds on Gromov width expressed via toric invariants

Application of minimal curve area bounds to toric manifolds

Extension of bounds from uniruled Kähler manifolds to toric varieties

Abstract

The Gromov width of a uniruled projective K\"ahler manifold can be bounded from above by the symplectic area of its minimal curves. We apply this result to toric varieties and thus get in this case upper bounds expressed in toric combinatorial invariants.