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Expressing Forms as a Sum of Pfaffians
Chiantini, Luca
2015
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e-ISSN
2464-8728
Abstract
Let A = (aij) be a symmetric non-negative integer 2k X 2k
matrix. A is homogeneous if aij + ail = an + akj for any choice of the
four indexes. Let A be a homogeneous matrix and let F be a general
form in C[xi,....xn] with 2deg(F) = trace(A). We look for the least
integer s(A), so that F = pfaff(M1) + ••• + pfaff(Ms(A)) where the
Mi = (Fim) are 2k X 2k skew-symmetric matrices of forms with degree
matrix A. We consider this problem for n = 4 and we prove that
s (A)_< k for all A.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
47 (2015)
Publisher
EUT Edizioni Università di Trieste
Languages
en
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