Some Applications of Multiplier Ideals

Abstract

The machinery developed in the previous chapter already has many substantial applications, and we present a number of these here. We start in the first section with several results involving singularities of divisors. In Section 10.2 we prove Matsusaka’s theorem following the approach of Siu and Demailly. The next section is devoted to a theorem of Nakamaye describing the base loci of big and nef divisors. Results and conjectures concerning global generation of adjoint linear series occupy Section 10.4, where in particular we prove the theorem of Angehrn and Siu. Finally, in Section 10.5 we discuss applications of Skoda’s theorem to the effective Nullstellensatz.