Stability of Equivariant Logarithmic Tangent Sheaves on Toric Varieties of Picard Rank Two

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.

arXiv commentModification of the document structure. To appear in "Annales de la facult{é} des sciences de Toulouse''