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On vector bundles over hyperk"ahler twistor spaces | | Indranil Biswas
; Artour Tomberg
; | | Date: |
3 Nov 2019 | | Abstract: | We study the holomorphic vector bundles $E$ on the twistor space
$mathrm{Tw}(M)$ of a compact simply connected hyperk"ahler manifold $M$. We
give a characterization of semistability of $E$ in terms of its restrictions to
the sections of the holomorphic twistor projection $pi ,:,
mathrm{Tw}(M),longrightarrow, mathbb{CP}^1$, and show that $E$ only admits
trivial holomorphic connections (and this only if $E$ is itself trivial). For
irreducible $E$ of prime rank, we prove that its restriction to the generic
fibre of $pi$ is stable. On the other hand, for $M$ a K3 surface, we construct
examples of irreducible bundles of any composite rank on $mathrm{Tw}(M)$ whose
restriction to every fibre of $pi$ is non-stable. We have a new method of
constructing irreducible bundles on hyperk"ahler twistor spaces, which is used
in constructing these examples. | | Source: | arXiv, 1911.0833 | | Services: | Forum | Review | PDF | Favorites | |
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