First irreducible rank-2 dHYM connections are constructed on the full flag manifold F₂, and rank-1 solutions outside the supercritical regime disprove conjectured stability conditions.
Stability for Line Bundles and Deformed Hermitian-Yang-Mills Equation on Some Elliptic Surfaces
2 Pith papers cite this work, alongside 10 external citations. Polarity classification is still indexing.
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abstract
We study the twisted ampleness criterion due to Collins, Jacob and Yau on surfaces, which is equivalent to the existence of solutions to the deformed Hermitian-Yang-Mills (dHYM) equation. When $X$ is a Weierstrass elliptic K3 surface, and $\omega$ an ample class such that $\omega$ lies in the span of a section class and the fiber class, we show that for a class of line bundles $L$ with fiber degree 1 and $\omega c_1(L)>0$, the twisted ampleness of $L$ respect to $\omega$, always implies the $\sigma_{\omega, 0}$-stability (Bridgeland stability) of $L$. This answers a question by Collins and Yau for a class of examples.
representative citing papers
Uses calibrations to protect examined non-supersymmetric AdS vacua in type II string theory from D-brane mediated decays, including abelian bound states.
citing papers explorer
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Deformed Hermitian-Yang-Mills equation on the manifold of full flags
First irreducible rank-2 dHYM connections are constructed on the full flag manifold F₂, and rank-1 solutions outside the supercritical regime disprove conjectured stability conditions.
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Stability of non-supersymmetric vacua from calibrations
Uses calibrations to protect examined non-supersymmetric AdS vacua in type II string theory from D-brane mediated decays, including abelian bound states.