Z-critical equations for holomorphic vector bundles on Kähler surfaces

2024/05/06 by Keller, Julien, Scarpa, Carlo · 2 citations
#14J60 #32W50 (Secondary) #53C07 (Primary) #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2405.03312

Abstract

We prove that the existence of a Z-positive and Z-critical Hermitian metric on a rank 2 holomorphic vector bundle over a compact Kähler surface implies that the bundle is Z-stable. As particular cases, we obtain stability results for the deformed Hermitian Yang-Mills equation and the almost Hermite-Einstein equation for rank 2 bundles over surfaces. We show examples of Z-unstable bundles and Z-critical metrics away from the large volume limit.

Cited by

• Polynomial stability conditions for vector bundles: Positivity, equivariance and blow-ups
• Polynomial Bridgeland Stability Conditions on the Category of Coherent Sheaves

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