2007/10/22 by Dmitri Panov, Julius Ross, Panov, Dmitri +1
Mathematics · #14C05 #14L24 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #math.AG #msc:14C05 #msc:14L24
paper · pdf · doi:10.48550/arxiv.0710.4078
Published version
openalex publication_date 2007/10/22 · arxiv created 2008/08/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study slope stability of smooth surfaces and its connection with exceptional divisors. We show that a surface containing an exceptional divisor with arithmetic genus at least two is slope unstable for some polarisation. In the converse direction we show that slope stability of surfaces can be tested with divisors, and prove that for surfaces with non-negative Kodaira dimension any destabilising divisor must have negative self-intersection and arithmetic genus at least two. We also prove that a destabilising divisor can never be nef, and as an application give an example of a surface that is slope stable but not K-stable.