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arXiv · 2210.02926

Formats of 6 x 6 skew matrices of linear forms with vanishing Pfaffian

Christian Böhning·Hans-Christian Graf von Bothmer
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Abstract

We show that every skew-symmetric 6 x 6 matrix of linear forms with vanishing Pfaffian is congruent to one of finitely many types of matrices, each of which is characterised by a specific pattern of zeroes (and some other linear relations) among its entries. Such matrices are for example important for compactifying moduli spaces of stable rank 2 vector bundles with Chern classes c_1=0, c_2=2 on cubic threefolds.

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Christian Böhning, Hans-Christian Graf von Bothmer. 2022-10-06. Formats of 6 x 6 skew matrices of linear forms with vanishing Pfaffian. https://arxiv.org/abs/2210.02926

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