2015/09/01 by Indranil Biswas, Biswas, Indranil, Georg Schumacher +1
Mathematics · #14J60 #32G13 #32L10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1509.00304
openalex publication_date 2015/09/01 · openalex created_date 2022/10/07 · openalex updated_date 2026/07/28
We investigate stable holomorphic vector bundles on a compact complex\nK "ahler manifold and more generally on an orbifold that is equipped with a\nK "ahler structure. We use the existence of Hermite-Einstein connections in\nthis set-up and construct a generalized Weil-Petersson form on the moduli space\nof stable vector bundles with fixed determinant bundle. We show that the\nWeil-Petersson form extends as a (semi-)positive closed current for\ndegenerating families that are restrictions of coherent sheaves. Such an\nextension will be called a Weil-Petersson current. When the orbifold is of\nHodge type, there exists a determinant line bundle on the moduli space; this\nline bundle carries a Quillen metric, whose curvature coincides with the\ngeneralized Weil-Petersson form. As an application we show that the determinant\nline bundle extends to a suitable compactification of the moduli space.\n