Full Ellipsoid Embeddings and Toric Mutations
Abstract
This article introduces a new method to construct volume-filling symplectic embeddings of 4-dimensional ellipsoids by employing polytope mutations in toric and almost-toric varieties. The construction uniformly recovers the full sequences for the Fibonacci Staircase of McDuff-Schlenk, the Pell Staircase of Frenkel-Muller and the Cristofaro-Gardiner-Kleinman's Staircase, and adds new infinite sequences of ellipsoid embeddings. In addition, we initiate the study of symplectic tropical curves for almost-toric fibrations and emphasize the connection to quiver combinatorics.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2020
- DOI:
- 10.48550/arXiv.2004.13232
- arXiv:
- arXiv:2004.13232
- Bibcode:
- 2020arXiv200413232C
- Keywords:
-
- Mathematics - Symplectic Geometry;
- Mathematics - Algebraic Geometry;
- 53D05;
- 53D20;
- 14M25
- E-Print:
- 57 Pages, 28 Figures. Mistake in Subsection 4.1 found that directly affects Theorem 1.8 and consequently part of the proof of Theorem 1.4. Theorem 1.8 cannot hold in the stated generality