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arXiv · 2609.28536

Toric Richardson Varieties and Slice Links

Thomas C. Martinez·Matthew J. Tyler
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Abstract

For type $A$ braid varieties, including Richardson varieties and positroid varieties, we prove that the standard torus has a dense orbit exactly when the associated link is smoothly slice. More generally, we relate the smooth slice genus to the codimension of a generic standard-torus orbit. For knots, this codimension equals twice the slice genus. We also characterize algebraic tori among open affine Richardson varieties and positroid patches by 2-crown avoidance in their Bruhat intervals. Finally, positroid links have equal Seifert and slice genera, so a positroid link is smoothly slice exactly when it is an unlink.

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Thomas C. Martinez, Matthew J. Tyler. 2026-09-22. Toric Richardson Varieties and Slice Links. https://arxiv.org/abs/2609.28536

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