Tangent Weights and Invariant Curves in Type A Bow Varieties

TL;DR

This paper classifies torus-invariant curves in type A Cherkis bow varieties, introduces a tangent weight formula, and uses combinatorial tools to analyze their geometric structure.

Contribution

It provides a complete classification of invariant curves and a novel tangent weight formula for type A bow varieties, advancing understanding of their geometric and combinatorial properties.

Findings

Complete classification of invariant curves

Development of a tangent weight formula

Application to example bow varieties

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).