Extremality with respect to the estimates of Dubreil-Campanella: Splitting theorems (Q1814223)

Let \(I\) be a 2-codimensional perfect homogeneous ideal in a polynomial algebra of finite type over an infinite base field. P. Dubreil in 1933 and G. Campanella in 1986 have given sharp upper and lower bounds for the number of forms of any given degree in a standard basis of \(I\) which is a minimal homogeneous basis ordered by increasing degrees. The authors now consider in their paper consequences of upper-bound-extremality in this situation and show among other things that it implies a splitting of the syzygy module of a standard basis of \(I\) into syzygy modules of the component ideals of \(I\).