• János Kollár
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 32)


The aim of this chapter is to discuss some auxiliary results that do not fit anywhere else. Section 1 considers rational curves on exceptional loci of maps. The main result (1.2) is a theorem of [Abhyankar56] which says that if f : X → Y is a birational morphism and Y is smooth, then every exceptional divisor of f is ruled. This is clear if resolution of indeterminacies holds for f -1, but the result can be proved using only some partial resolution results. The relevant assertion about resolutions (1.3) is contained in [Zariski39] and it is useful in many instances.


Line Bundle Exceptional Divisor Rational Curf Coherent Sheaf Cartier Divisor 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • János Kollár
    • 1
  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA

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