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

William W. Adams;  Philippe Loustaunau;  Victor P. Palamodov;  Daniele C. Struppa — 1997

Annales de l'institut Fourier

In this paper we prove that the projective dimension of ℳ n = R 4 / ⟨ A n ⟩ is 2 n - 1 , where R is the ring of polynomials in 4 n variables with complex coefficients, and ⟨ A n ⟩ is the module generated by the columns of a 4 × 4 n 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 ℛ of regular functions has flabby dimension 2 n - 1 , and we prove a cohomology vanishing theorem for open...

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