Geodesic
On the closures of orbits of fourth order matrix pencils
Izvestiya. Mathematics , Tome 66 (2002) no. 5, pp. 1047-1055.

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We state a simple criterion for nilpotency of an $n\times n$ matrix pencil with respect to the action of $\operatorname{SL}_n(\mathbb C)\times \operatorname{SL}_n(\mathbb C) \times\operatorname{SL}_2(\mathbb C)$. We explicitly classify the orbits of matrix pencils for $n=4$ and describe the hierarchy of closures of nilpotent orbits. We also prove that the algebra of invariants of the action of $\operatorname{SL}_n(\mathbb C)\times \operatorname{SL}_n(\mathbb C)\times\operatorname{SL}_2(\mathbb C)$ on $\mathbb C_n\otimes\mathbb C_n\otimes\mathbb C_2$ is naturally isomorphic to the algebra of invariants of binary forms of degree $n$ with respect to the action of $\operatorname{SL}_2(\mathbb C)$. 
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D. D. Pervouchine. On the closures of orbits of fourth order matrix pencils. Izvestiya. Mathematics , Tome 66 (2002) no. 5, pp. 1047-1055. http://geodesic.mathdoc.fr/item/IM2_2002_66_5_a4/

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