The deformed Vortex equations and equivariant stability conditions

2026/07/20 by Tristan C. Collins, Yukai Zhang
#math.DG #math.AG

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Abstract

We study the higher rank deformed Hermitian-Yang-Mills (dHYM) equations for SU(2)-equivariant holomorphic vector bundles over X× ℙ¹ for X a compact Riemann surface. For a class of vector bundles of vortex type, we establish the equivalence between existence of solutions to higher rank dHYM equations and an appropriate notion of algebro-geometric stability, called Z-stability. We show that Z-stability is implied by, and conjecturally equivalent to, Bridgeland stability in D^b\rm Coh^SU(2)(X× ℙ¹).

Related

• Stability and the deformed Hermitian-Yang-Mills equation
• Z-critical connections and Bridgeland stability conditions
• DHYM connections on higher rank holomorphic vector bundles over ℙ(T_ℙ²)
• J-equation on holomorphic vector bundles
• Deformed Hermitian Yang-Mills equation on rational homogeneous varieties