On the Hilbert Function of Determinants Rings and Their Canonical Module

@inproceedings{Conca2010OnTH,
  title={On the Hilbert Function of Determinants Rings and Their Canonical Module},
  author={Aldo Conca and J{\"u}rgen Herzog},
  year={2010}
}
We determine the Hubert function of a determinantal ring and of its canonical module using a combinatorial result of Krattenthaler. This gives a new proof of Abhyankar's formula. Let AT be a field and X = (X¡j) be an m x «-matrix of indeterminates, with m < n . We denote by K[X] the polynomial ring over K in the indeterminates Xij and by Ir+x(X) the ideal in K[X] generated by the r+ 1 -minors of X and set Rr+x=K[X]/Ir+x(X). The purpose of this note is to derive a compact formula for the Hubert… CONTINUE READING