Divisor class group and canonical class of rings defined by ideals of pfaffians

Abstract

In this paper we study the rings defined by ideals of pfaffians of a skew symmetric matrix of indeterminates. We analyze the case in which the pfaffians are not necessarily of fixed size. We prove that such rings are Cohen-Macaulay normal domains and we compute the divisor class group and the canonical class. It allows us to determine which of our rings are Gorenstein.

Partially supported ba a grant of Istituto Nazionale Alta Matematica, Italy, and by DFG, Germany

Partially supported ba a grant of Istituto Nazionale Alta Matematica, Italy, and by DFG, Germany

Notes

Partially supported ba a grant of Istituto Nazionale Alta Matematica, Italy, and by DFG, Germany