Hartog ’ s phenomenon for polyregular functions and projective dimension of related modules over a polynomial ring

@inproceedings{Loustaunau1995HartogS,
title={Hartog ’ s phenomenon for polyregular functions and projective dimension of related modules over a polynomial ring},
author={Philippe Loustaunau},
year={1995}
}

In this paper we prove that the projective dimension of Mn = R 4 =hAni is 2n ? 1, where R is the ring of polynomials in 4n variables with complex coeecients, and hAni is the module generated by the columns of a 44n matrix which arises as the Fourier transform of the matrix of diierential operators associated with the regularity condition for a function of n quater-nionic variables. As a corollary we show that the sheaf R of regular functions has abby dimension 2n?1, and we prove a cohomology… CONTINUE READING