Toric Richardson 簇与切片链环
Toric Richardson Varieties and Slice Links
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中文总结 AI 辅助
本文证明类型A辫子簇中标准环面有稠密轨道当且仅当相关链环光滑可切片，并将光滑切片亏格与轨道余维数联系，刻画代数环面，证明positroid链环的切片性等价于平凡性。
中文摘要 AI 辅助
对于类型 $A$ 的辫子簇，包括 Richardson 簇和 positroid 簇，我们证明了标准环面具有稠密轨道当且仅当相关的链环是光滑可切片的。更一般地，我们将光滑切片亏格与一般标准环面轨道的余维数联系起来。对于纽结，该余维数等于切片亏格的两倍。我们还通过其 Bruhat 区间中的 2-皇冠回避来刻画开仿射 Richardson 簇和 positroid 片中的代数环面。最后，positroid 链环具有相等的 Seifert 亏格和切片亏格，因此 positroid 链环是光滑可切片的当且仅当它是平凡链环。
英文摘要
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.
