Extremal zero-dimensional subschemes of image2 Original Research Article

Given a zero-dimensional subscheme image of image2, we bound the number of points in the support of image which have maximal degree in image. For reduced schemes image, this yields a lower bound for the colength of the conductor image of the homogeneous coordinate ring R of image in its integral closure image. This bound is attained by Castelnuovo sets for which we calculate image explicitly. Using the canonical decomposition of image, we also show a sharp upper bound for image. Applications include estimates for the singularity degree image and the superabundance image—image of image.