Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 21 (2025), 016, 33 pages      arXiv:2310.04973      https://doi.org/10.3842/SIGMA.2025.016

Tangent Weights and Invariant Curves in Type A Bow Varieties

Alexander Foster a and Yiyan Shou b
a) Department of Mathematics, University of North Carolina at Chapel Hill, NC, USA
b) Independent Researcher, Alexandria, VA, USA

Received December 08, 2023, in final form February 20, 2025; Published online March 09, 2025

Abstract
This paper provides a complete classification of torus-invariant curves in Cherkis bow varieties of type A. We develop combinatorial codes for compact and noncompact invariant curves involving the butterfly diagrams, Young diagrams, and binary contingency tables. As a key intermediate step, we also develop a novel tangent weight formula. Finally, we apply this new machinery to example bow varieties to demonstrate how to obtain their 1-skeletons (union of fixed points and invariant curves).

Key words: Cherkis bow varieties; invariant curves; butterfly surgery; Young diagrams.

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