Geodesic
Number of components of the nullcone
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematics, mechanics, and mathematical physics, Tome 290 (2015), pp. 95-101

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For every pair $(G,V)$ where $G$ is a connected simple linear algebraic group and $V$ is a simple algebraic $G$-module with a free algebra of invariants, the number of irreducible components of the nullcone of unstable vectors in $V$ is found. 
@article{TM_2015_290_a7,
     author = {V. L. Popov},
     title = {Number of components of the nullcone},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {95--101},
     publisher = {mathdoc},
     volume = {290},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2015_290_a7/}
}
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V. L. Popov. Number of components of the nullcone. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematics, mechanics, and mathematical physics, Tome 290 (2015), pp. 95-101. http://geodesic.mathdoc.fr/item/TM_2015_290_a7/