The Boden-Hu conjecture holds precisely up to rank 8

2003/10/10 by Norbert Hoffmann
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14D20 #msc:14H60

paper · pdf · doi:10.1007/s00208-004-0567-5

published as Math. Ann. 330 (2004), 729 - 746 · 17 pages

arxiv created 2003/10/10 · openalex publication_date 2004/08/09 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29

Abstract

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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