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Splitting conjectures for uniform flag bundles. (English) Zbl 1442.14131

Some years ago the authors developed the notion of uniformity and splitting for principal bundles, not just for vector bundles [R. Muñoz et al., “On uniform flag bundles on Fano manifolds”, Preprint, arXiv:1610:05930]. Here they raise several conjectures on the splitting of low rank principal bundles and prove them for principal bundles associated to classical group. It would be nice to know it in positive characteristic, but probably this must first done in more elementary cases.

MSC:

14J45 Fano varieties
14E30 Minimal model program (Mori theory, extremal rays)
14M15 Grassmannians, Schubert varieties, flag manifolds
14M17 Homogeneous spaces and generalizations
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