Geodesic
Stability of Equivariant Vector Bundles over Toric Varieties
Documenta mathematica, Tome 25 (2020), pp. 1787-1833
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We give a complete answer to the question of (semi)stability of tangent bundles on any nonsingular complex projective toric variety with Picard number 2 by using combinatorial criterion of (semi)stability of an equivariant sheaf. We also give a complete answer to the question of (semi)stability of tangent bundles on all toric Fano 4-folds with Picard number ≤3 which are classified by Batyrev [1]. We construct a collection of equivariant indecomposable rank 2 vector bundles on Bott towers and pseudo-symmetric toric Fano varieties. Furthermore, in case of Bott towers, we show the existence of an equivariant stable rank 2 vector bundle with certain Chern classes with respect to a suitable polarization.
DOI : 10.4171/dm/785
Classification : 14J45, 14J60, 14M25
Mots-clés : toric variety, equivariant sheaf, (semi)stability, Bott tower, pseudo-symmetric variety, indecomposable vector bundle 
@article{10_4171_dm_785,
     author = {Jyoti Dasgupta and Arijit Dey and Bivas Khan},
     title = {Stability of {Equivariant} {Vector} {Bundles} over {Toric} {Varieties}},
     journal = {Documenta mathematica},
     pages = {1787--1833},
     year = {2020},
     volume = {25},
     doi = {10.4171/dm/785},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/785/}
}
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Jyoti Dasgupta; Arijit Dey; Bivas Khan. Stability of Equivariant Vector Bundles over Toric Varieties. Documenta mathematica, Tome 25 (2020), pp. 1787-1833. doi: 10.4171/dm/785

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