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The GIT of 4x3x3 tensors (determinantal cubic surfaces)
A general $4\times3\times3$ tensor defines three determinantal varieties in $\mathbb{P}^3$ and $\mathbb{P}^2$ and $\mathbb{P}^2$ where it drops rank: a cubic surface and two length 6 subschemes. We study the Geometric Invariant Theory (GIT) quotient of $\mathbb{P}(\mathbb{C}^4\otimes\mathbb{C}^3\oti
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