2003/09/02 by Vasile Brinzanescu, Vasile Brînzănescu, Brinzanescu, Vasile +2
Mathematics · #14D22 #14F05 #14J27 #14J60 #32J15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #math.AG #math.CV #msc:14D22 #msc:14F05 #msc:14J27 #msc:14J60 #msc:32J15
paper · pdf · doi:10.48550/arxiv.math/0309031
13 pages
arxiv created 2003/09/02 · openalex publication_date 2003/09/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study holomorphic rank-2 vector bundles on non-K" ahler elliptic surfaces. Our main tool for analysing these bundles is of course the spectral cover. However, given the non-Kähler condition, the elliptic surfaces we are considering do not have sections and gerbes naturally arise in this context. The spectral construction presented in this paper is a modification of the Fourier-Mukai transform for elliptic fibrations without a section. After examining some of the properties of this Fourier-Mukai transform, we give a complete classification of vector bundles on these surfaces.