Stability of equivariant vector bundles over toric varieties
Algebraic Geometry
2019-10-31 v1
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.
Cite
@article{arxiv.1910.13964,
title = {Stability of equivariant vector bundles over toric varieties},
author = {Jyoti Dasgupta and Arijit Dey and Bivas Khan},
journal= {arXiv preprint arXiv:1910.13964},
year = {2019}
}