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Title: Expressing Forms as a Sum of Pfaffians
Authors: Chiantini, Luca
Issue Date: 2015
Publisher: EUT Edizioni Università di Trieste
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
47 (2015)
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.
Type: Article
ISSN: 0049-4704
eISSN: 2464-8728
DOI: 10.13137/0049-4704/11218
Appears in Collections:Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics vol.47 (2015)

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