On the density function on moduli spaces of toric 4-manifolds

Alessio Figalli; Álvaro Pelayo

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arXiv · 1408.1462

On the density function on moduli spaces of toric 4-manifolds

Alessio Figalli·Álvaro Pelayo

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Abstract

The optimal density function assigns to each symplectic toric manifold $M$ a number $0 < d \leq 1$ obtained by considering the ratio between the maximum volume of $M$ which can be filled by symplectically embedded disjoint balls and the total symplectic volume of $M$. In the toric version of this problem, $M$ is toric and the balls need to be embedded respecting the toric action on $M$. The goal of this note is first to give a brief survey of the notion of toric symplectic manifold and the recent constructions of moduli space structure on them, and recall how to define a natural density function on this moduli space. Then we review previous works which explain how the study of the density function can be reduced to a problem in convex geometry, and use this correspondence to to give a simple description of the regions of continuity of the maximal density function when the dimension is $4$.

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Alessio Figalli, Álvaro Pelayo. 2014-08-07. On the density function on moduli spaces of toric 4-manifolds. https://arxiv.org/abs/1408.1462

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