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Abstract: Motivated by the Donaldson–Uhlenbeck–Yau theorem, a common strategy for studying gauge-theoretic equations is to relate them to a suitable notion of stability. For any choice of polynomial central charge Z over a closed Kähler manifold X, one can define a Z-critical equation for connections on a holomorphic vector bundle E→X. In the large volume regime, the existence of solutions to this equation is equivalent to the asymptotic Z-stability (aZ-stability) of E.

While all (Mumford) stable bundles are necessarily aZ-stable, this talk explores the construction of bundles that are aZ-stable but not Mumford stable. I will present a construction of such bundles over projective surfaces in the specific case where the Z-critical equation corresponds to the deformed Hermitian–Yang–Mills (dHYM) equation.