1996/07/04 by Bernd Kreussler, Bernd Kreußler, Kreussler, Bernd
Mathematics · #32L25 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Finite Group Theory Research #alg-geom #dg-ga #math.AG #math.DG #msc:32L25
paper · pdf · doi:10.48550/arxiv.alg-geom/9607007
23 pages LaTeX 2e
arxiv created 1996/07/04 · openalex publication_date 1996/07/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the algebraic dimension of twistor spaces of positive type over 4\bbfP2. We show that such a twistor space is Moishezon if and only if its anticanonical class is not nef. More precisely, we show the equivalence of being Moishezon with the existence of a smooth rational curve having negative intersection number with the anticanonical class. Furthermore, we give precise information on the dimension and base locus of the fundamental linear system |-1/2K|. This implies, for example, dim|-1/2K|≤ a(Z). We characterize those twistor spaces over 4\bbfP2, which contain a pencil of divisors of degree one by the property dim|-1/2K| = 3.