Seshadri constants of equivariant vector bundles on toric varieties

Seshadri constants of equivariant vector bundles on toric varieties

“…Note that the discriminant of E ⊗ O(D) is non-zero. Also for c 1,2 ≥ 2, this bundle is unstable with respect to the anticanonical divisor and it is stable when c 1,2 = 1 (see [DDK,Corollary 4.2.7]).…”

“…Hence, the filtrations (E, {E v j (i)} j=1,...,4 ) correspond to a rank 2 equivariant indecomposable vector bundle on X 2 , say E (see [DDK,Proposition 6.1.1]).…”

“…Note that for a suitable choice of polarization on X 2 , the vector bundle E becomes stable (see [DDK,Proposition 6.1.5]). If discriminant of E was zero then by [BG,Theorem 2.5], we can conclude that (E ⊗O(D))| D ′ 1 is semistable, which is not the case.…”

“…Again, for a suitable choice of polarization on X 3 , the vector bundle E becomes stable (see [DDK, Proposition 6.1.5]). We observe that discriminant of E is non-zero using the same argument as in Example 5.5.…”

Stability of equivariant logarithmic tangent sheaves on toric varieties of Picard rank two

“…By using the equivariant structure of the tangent bundle, Hering-Nill-Süss in [HNS19] and Dasgupta-Dey-Khan in [DDK20] studied slope-stability of the tangent bundle T X of a smooth projective toric variety X of Picard rank one or two. Inspired by Iitaka's philosophy, in this paper, we extend the result of [HNS19] and [DDK20] to the case of log pairs (X, D).…”