2010/12/31 by Peter B. Gothen, André Oliveira, André G. Oliveira · 13 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Compact Riemann surface #Fiber #Fiber bundle #Geometry and complex manifolds #Higgs boson #Line bundle #Moduli space #Rank (graph theory) #Riemann surface #Singularity #math.AG #msc:14H40 #msc:14H60
paper · pdf · doi:10.1093/imrn/rns020
published in International Mathematics Research Notices 2013(5), 1079-1121 (Oxford University Press) · 28 pages; v3; minor changes: added Proposition 3.7 and main Theorem 8.1 now also refers the fibre over zero; final version
arxiv created 2012/02/03 · openalex publication_date 2012/02/17 · openalex created_date 2016/06/24 · arxiv updated 2017/10/05 · openalex updated_date 2026/08/05
We give a description of the singular fiber of the Hitchin map on the moduli space of L-twisted Higgs pairs of rank 2 with fixed determinant bundle, when the corresponding spectral curve has any singularity of type Am−1. In particular, we prove directly that this fiber is connected.