Geodesic
The structure of the variety of pairs of commuting pencils of symmetric matrices
Izvestiya. Mathematics, Tome 20 (1983) no. 2, pp. 391-410 
A. N. Tyurin. The structure of the variety of pairs of commuting pencils of symmetric matrices. Izvestiya. Mathematics, Tome 20 (1983) no. 2, pp. 391-410. http://geodesic.mathdoc.fr/item/IM2_1983_20_2_a8/
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     title = {The structure of the variety of pairs of commuting pencils of symmetric matrices},
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This paper describes the components of the variety of classes of pairs of commuting pencils of symmetric matrices. Bibliography: 7 titles.

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[2] Barth W., “Irreducibility of the space of mathematical instant on bundles with rank 2 and $c_2=4$”, Math. Ann., 258:1 (1981), 81–106 | DOI | MR | Zbl

[3] Grothendieck A., “Les schemas de Hilbert”, Sem. Bourbaki (1960–1961), 221

[4] Mumford D., “An algebro-geometric construction of commuting operators and of solutions to the Toda lattice equation, Korteweg de Vries equation and related non-linear equations”, Intl. Symp. on Algebraic Geometry Kyoto, 1977, 145–153

[5] Tyurin A. N., “O peresechenii kvadrik”, Uspekhi matem. nauk, 30:6 (1975), 51–100 | MR

[6] Tyurin A. N., “Geometriya osobennostei obschei kvadratichnoi formy”, Izv. AN SSSR. Ser. matem., 44:5 (1980), 1200–1227 | MR

[7] Wall C. T. C., “Nets of quadrics and theta-characteristics of singular curves”, Phil. Trans. of R. S. Lond.(A), 289 (1978), 229–269 | DOI | MR | Zbl