Expressing Forms as a sum of Pfaffians
Algebraic Geometry
2015-03-17 v1
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 general form in C[x_1, \dots x_n] with 2deg(F) = trace(A). We look for the least integer, s(A), so that F= pfaff(M_1) + \cdots + pfaff(M_{s(A)}), where the M_i's 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.
Cite
@article{arxiv.1503.04408,
title = {Expressing Forms as a sum of Pfaffians},
author = {Luca Chiantini},
journal= {arXiv preprint arXiv:1503.04408},
year = {2015}
}