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arXiv · 1207.6299

Linear spaces of matrices of constant rank and instanton bundles

Ada Boralevi·Daniele Faenzi·Emilia Mezzetti
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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.

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Ada Boralevi, Daniele Faenzi, Emilia Mezzetti. 2012-07-26. Linear spaces of matrices of constant rank and instanton bundles. https://arxiv.org/abs/1207.6299

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