The Boden-Hu conjecture holds precisely up to rank eight

Details The Boden-Hu conjecture holds precisely up to rank eight The Boden-Hu conjecture holds precisely up to rank eight

2003-10-10

arxiv.org/abs/math/0310160v1

Math. Ann. 330 (2004), 729 - 746

Mathematics

Algebraic Geometry

17 pages

Scientific paper

10.1007/s00208-004-0567-5

Consider moduli schemes of vector bundles over a smooth projective curve endowed with parabolic structures over a marked point. Boden and Hu observed that a slight variation of the weights leads to a desingularisation of the moduli scheme, and they conjectured that one can always obtain a small resolution this way. The present text proves this conjecture in some cases (including all bundles of rank up to eight) and gives counterexamples in all other cases (in particular in every rank beyond eight). The main tool is a generalisation of Ext-groups involving more than two quasiparabolic bundles.

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