Semicontinuity of the {\L}ojasiewicz exponent
  We prove that the {\L}ojasiewicz exponent $l_0(f)$ of a finite holomorphic germ $f:(C^n,0)\to(C^n,0)$ is lower semicontinuous in any multiplicity-constant deformation of $f$. 
Arkadiusz Ploski
math.AG