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Stability for Line Bundles and Deformed Hermitian-Yang-Mills Equation on Some Elliptic Surfaces
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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.
Forward citations
Cited by 3 Pith papers
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The deformed Vortex equations and equivariant stability conditions
On vortex-type SU(2)-equivariant bundles over a product of a curve with P¹, solvability of the deformed Hermitian–Yang–Mills system is equivalent to Z-stability, and Bridgeland stability implies Z-stability.
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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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Polynomial stability conditions for vector bundles: Positivity, equivariance and blow-ups
P-critical connections generalize Z-critical connections; on toric varieties P-positivity is checked finitely, and uniform P-positivity survives point blow-ups.
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