Stability of Equivariant Vector Bundles over Toric Varieties

  • Jyoti Dasgupta

    Department of Mathematics, Indian Institute of Technology-Madras, Chennai, India
  • Arijit Dey

    Department of Mathematics, Indian Institute of Technology-Madras, Chennai, India
  • Bivas Khan

    Department of Mathematics, Indian Institute of Technology-Madras, Chennai, India
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Abstract

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 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.

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Jyoti Dasgupta, Arijit Dey, Bivas Khan, Stability of Equivariant Vector Bundles over Toric Varieties. Doc. Math. 25 (2020), pp. 1787–1833

DOI 10.4171/DM/785