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

Adams, William W., et al. "Hartog's phenomenon for polyregular functions and projective dimension of related modules over a polynomial ring." Annales de l'institut Fourier 47.2 (1997): 623-640. <http://eudml.org/doc/75240>.

@article{Adams1997,
abstract = {In this paper we prove that the projective dimension of $\{\cal M\}_n=R^4/\langle A_n\rangle $ is $2n-1$, where $R$ is the ring of polynomials in $4n$ variables with complex coefficients, and $\langle A_n\rangle $ is the module generated by the columns of a $4 \times 4n$ matrix which arises as the Fourier transform of the matrix of differential operators associated with the regularity condition for a function of $n$ quaternionic variables. As a corollary we show that the sheaf $\{\cal R\}$ of regular functions has flabby dimension $2n-1$, and we prove a cohomology vanishing theorem for open sets in the space $\{\Bbb H\}^n$ of quaternions. We also show that $\{\rm Ext\}^j(\{\cal M\}_n,R)=0$, for $j=1, \dots ,2n-2$ and $\{\rm Ext\}^\{2n-1\}(\{\cal M\}_n,R) \ne 0,$ and we use this result to show the removability of certain singularities of the Cauchy–Fueter system.},
author = {Adams, William W., Loustaunau, Philippe, Palamodov, Victor P., Struppa, Daniele C.},
journal = {Annales de l'institut Fourier},
keywords = {Hartog's phenomenon; regular functions; projective dimension; Cauchy-Fueter; system quaternions},
language = {eng},
number = {2},
pages = {623-640},
publisher = {Association des Annales de l'Institut Fourier},
title = {Hartog's phenomenon for polyregular functions and projective dimension of related modules over a polynomial ring},
url = {http://eudml.org/doc/75240},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Adams, William W.
AU - Loustaunau, Philippe
AU - Palamodov, Victor P.
AU - Struppa, Daniele C.
TI - Hartog's phenomenon for polyregular functions and projective dimension of related modules over a polynomial ring
JO - Annales de l'institut Fourier
PY - 1997
PB - Association des Annales de l'Institut Fourier
VL - 47
IS - 2
SP - 623
EP - 640
AB - In this paper we prove that the projective dimension of ${\cal M}_n=R^4/\langle A_n\rangle $ is $2n-1$, where $R$ is the ring of polynomials in $4n$ variables with complex coefficients, and $\langle A_n\rangle $ is the module generated by the columns of a $4 \times 4n$ matrix which arises as the Fourier transform of the matrix of differential operators associated with the regularity condition for a function of $n$ quaternionic variables. As a corollary we show that the sheaf ${\cal R}$ of regular functions has flabby dimension $2n-1$, and we prove a cohomology vanishing theorem for open sets in the space ${\Bbb H}^n$ of quaternions. We also show that ${\rm Ext}^j({\cal M}_n,R)=0$, for $j=1, \dots ,2n-2$ and ${\rm Ext}^{2n-1}({\cal M}_n,R) \ne 0,$ and we use this result to show the removability of certain singularities of the Cauchy–Fueter system.
LA - eng
KW - Hartog's phenomenon; regular functions; projective dimension; Cauchy-Fueter; system quaternions
UR - http://eudml.org/doc/75240
ER -