Linear spaces of matrices of constant rank and instanton bundles
arXiv:1207.6299
Abstract
We present a new method to study 4-dimensional linear spaces of skew-symmetric matrices of constant co-rank 2, based on rank 2 vector bundles on P^3 and derived category tools. The method allows one to prove the existence of new examples of size 10x10 and 14x14 via instanton bundles of charge 2 and 4 respectively, and provides an explanation for what used to be the only known example (Westwick 1996). We also give an algorithm to construct explicitly a matrix of size 14 of this type.
Revised version, 22 pages. Brief intro to derived category tools and details to proof of Lemma 3.5 added, some typos corrected