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arXiv · 2004.13232

Full Ellipsoid Embeddings and Toric Mutations

Roger Casals·Renato Vianna
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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.

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Roger Casals, Renato Vianna. 2020-04-28. Full Ellipsoid Embeddings and Toric Mutations. https://arxiv.org/abs/2004.13232

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