2000/09/15 by Robert Friedman, John W. Morgan, Friedman, Robert +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG
paper · pdf · doi:10.48550/arxiv.math/0009155
LaTeX, a reference is added
openalex publication_date 2000/09/15 · arxiv created 2000/09/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a del Pezzo surface of degree d between 1 and 6, possibly with rational double points, we construct a "tautological" holomorphic G-bundle over X, where G is a reductive group which is an appropriate conformal form of the simply connected complex linear group whose coroot lattice is isomorphic to the primitive cohomology of the minimal resolution of X. For example, in case d=3 and X is a smooth cubic surface, the rank 27 vector bundle over X associated to the G-bundle constructed above and the standard 27-dimensional representation of E6 is a direct sum of the line bundles associated to the 27 lines on X. We also discuss the restriction of the G-bundle to smooth hyperplane sections.