The resolution property of algebraic surfaces

2010/01/31 by Philipp Gross
Computer Science · Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic cycle #Algebraic number #Algebraic surface #Class (philosophy) #Coherent sheaf #Commutative Algebra and Its Applications #Mathematical analysis #Mathematics #Polynomial and algebraic computation #Property (philosophy) #Pure mathematics #Quotient #Resolution (logic) #Ring (chemistry) #Sheaf #math.AG #msc:14C20 #msc:14F05 #msc:14J60

paper · pdf · doi:10.1112/s0010437x11005628

published as Compositio Math. 148 (2012) 209-226 · 19 pages

arxiv created 2010/08/16 · openalex publication_date 2011/11/09 · arxiv updated 2019/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Abstract We prove that on separated algebraic surfaces every coherent sheaf is a quotient of a locally free sheaf. This class contains many schemes that are neither normal, reduced, quasiprojective nor embeddable into toric varieties. Our methods extend to arbitrary two-dimensional schemes that are proper over an excellent ring.

Citations

• Théorie des Intersections et Théorème de Riemann-Roch
• Toward a Numerical Theory of Ampleness
• Éléments de géométrie algébrique : IV. Étude locale des schémas et des morphismes de schémas, Première partie
• Éléments de géométrie algébrique : II. Étude globale élémentaire de quelques classes de morphismes
• Éléments de géométrie algébrique : I. Le langage des schémas