Lattice Formulas For Rational SFT Capacities
Abstract
We initiate the study of the rational SFT capacities of Siegel using tools in toric algebraic geometry. In particular, we derive new (often sharp) bounds for the RSFT capacities of a strongly convex toric domain in dimension . These bounds admit descriptions in terms of both lattice optimization and (toric) algebraic geometry. Applications include (a) an extremely simple lattice formula for for many RSFT capacities of a large class of convex toric domains, (b) new computations of the Gromov width of a class of product symplectic manifolds and (c) an asymptotics law for the RSFT capacities of all strongly convex toric domains.
Keywords
Cite
@article{arxiv.2106.07920,
title = {Lattice Formulas For Rational SFT Capacities},
author = {Julian Chaidez and Ben Wormleighton},
journal= {arXiv preprint arXiv:2106.07920},
year = {2021}
}
Comments
35 pages, 11 figures, comments welcome! Made corrections to the statements of Lemma 10 and Theorem 5. Added more details to proofs in Section 4.5