A note on relative dimensions of rings and conductors in function fields Original Research Article

Let image be the local ring at a curve singularity and let image be a ring such that image subset of or equal to image subset of or equal to image, where image denotes the integral closure of image in its field of fractions. Let (image:image) denote the conductor of image in image. We compare here the dimensions (over the base field) of image and image. We relate this with the intersection numbers of branches at the singularity.