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arXiv · 2005.06593

Pfaffian representations of cubic threefolds

Gaia Comaschi
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Abstract

Given a cubic hypersurface $X\subset \mathbb{P}^4$, we study the existence of Pfaffian representations of $X$, namely of $6\times 6$ skew-symmetric matrices of linear forms $M$ such that $X$ is defined by the equation $Pf(M)=0$. It was known that such a matrix always exists whenever $X$ is smooth. Here we prove that the same holds whenever $X$ is singular, hence that every cubic threefold is Pfaffian.

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Gaia Comaschi. 2020-05-13. Pfaffian representations of cubic threefolds. https://arxiv.org/abs/2005.06593

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