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arXiv · 1910.13964

Stability of equivariant vector bundles over toric varieties

Jyoti Dasgupta·Arijit Dey·Bivas Khan
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Abstract

We give a complete answer to the question of (semi)stability of tangent bundle of any nonsingular projective complex toric variety with Picard number 2 by using combinatorial crietrion of (semi)stability of an equivariant sheaf. We also give a complete answer to the question of (semi)stability of tangent bundle of all toric Fano 4-folds with Picard number (\leq) 3 which are classified by Batyrev \cite{batyrev}. We have constructed a collection of equivariant indecomposable rank 2 vector bundles on Bott tower and pseudo-symmetric toric Fano varieties. Further in case of Bott tower, we have shown the existence of an equivariant stable rank 2 vector bundle with certain Chern classes with respect to a suitable polarization.

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Jyoti Dasgupta, Arijit Dey, Bivas Khan. 2019-10-30. Stability of equivariant vector bundles over toric varieties. https://arxiv.org/abs/1910.13964

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