DERIVATIONS PRESERVING A MONOMIAL IDEAL

Let I be a monomial ideal in a polynomial ring A = k[x(1),...,x(n)] over a field k of characteristic 0, T-A/k(I) be the module of I-preserving k-derivations oil A and G be the n-dimensional algebraic torus on k. We compute the weight spaces of T-A/k(I) considered as a representation of G. Using this, we show that T-A/k(I) preserves the integral closure of I and the multiplier ideals of I.