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Stability of Equivariant Logarithmic Tangent Sheaves on Toric Varieties of Picard Rank Two
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abstract
For an equivariant log pair $(X, D)$ where $X$ is a normal toric variety and $D$ a reduced Weil divisor, we study slope-stability of the logarithmic tangent sheaf $\mathcal{T}_{X}(- \log D)$. We give a complete description of divisors $D$ and polarizations $L$ such that $\mathcal{T}_{X}(- \log D)$ is (semi)stable with respect to $L$ when $X$ has a Picard rank one or two.
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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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