Calculations with multiplier ideals.

Abstract

In this thesis, we present some results which allow for the explicit calculation of multiplier ideals. Specifically, we compute the multiplier ideal of a monomial ideal. For a general section <italic>f</italic> of an ideal sheaf a , the multiplier ideals of <italic>Div</italic> (<italic>f</italic>) are essentially the same as those of a . For a monomial, we give an explicit nondegeneracy condition for <italic>f</italic> which guarantees that <italic>f</italic> is general enough. We then discuss several applications of these calculations.