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arXiv · 2104.00892

A classification of scalar-flat toric K\"ahler instantons in dimension 4

Brian Weber
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Abstract

We classify all scalar-flat toric K\"ahler 4-manifolds under either of two asymptotic conditions: that the action fields decay slowly (or at all), or that the curvature decay is quadratic; for example we fully classify instantons that have any of the ALE-F-G-H asymptotic types. The momentum functions satisfy a degenerate elliptic equation, and under either asymptotic condition the image of the moment map is closed. Using a recent Liouville theorem for degenerate-elliptic equations, we classify all possibilities for the momentum functions, and from this, all possible metrics.

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Brian Weber. 2021-04-02. A classification of scalar-flat toric K\"ahler instantons in dimension 4. https://arxiv.org/abs/2104.00892

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