Let A= (a_ij) be a symmetric non-negative integer 2k x 2k matrix. A is homogeneous if a_ij + a_kl=a_il + a_kj for any choice of the four indexes. Let A be a homogeneous matrix and let F be a emph{general} form in C[x_1, ..., x_n] with 2 deg(F) = trace(A). We look for the least integer, s(A), so that F = pfaff(M_1) + ... + pfaff(M_s(A)), where the M_i = (F^i_lm) 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+1 for all A.
Chiantini, L. (2015). Expressing forms as a sum of pfaffians. RENDICONTI DELL'ISTITUTO DI MATEMATICA DELL'UNIVERSITÀ DI TRIESTE, 47, 45-57 [10.13137/0049-4704/11218].
Expressing forms as a sum of pfaffians
Chiantini, Luca
2015-01-01
Abstract
Let A= (a_ij) be a symmetric non-negative integer 2k x 2k matrix. A is homogeneous if a_ij + a_kl=a_il + a_kj for any choice of the four indexes. Let A be a homogeneous matrix and let F be a emph{general} form in C[x_1, ..., x_n] with 2 deg(F) = trace(A). We look for the least integer, s(A), so that F = pfaff(M_1) + ... + pfaff(M_s(A)), where the M_i = (F^i_lm) 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+1 for all A.File | Dimensione | Formato | |
---|---|---|---|
RIMUT_47_05_Chiantini.pdf
accesso aperto
Tipologia:
PDF editoriale
Licenza:
PUBBLICO - Pubblico con Copyright
Dimensione
270.42 kB
Formato
Adobe PDF
|
270.42 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
https://hdl.handle.net/11365/991365