Geodesic
The homology groups of the variety of complete pairs $X_{13}$ of zero-dimensional subschemes of lengths~1 and~3 of projective space
Sbornik. Mathematics, Tome 191 (2000) no. 11, pp. 1693-1705

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Using the action of the one-dimensional diagonal torus group, we obtain the Betti numbers (the ranks of the homology groups as free modules) of the variety of complete pairs $X_{13}$ of zero-dimensional subschemes of lengths 1 and 3 of complex projective space. 
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     author = {N. V. Timofeeva},
     title = {The homology groups of the variety of complete pairs $X_{13}$ of zero-dimensional subschemes of lengths~1 and~3 of projective space},
     journal = {Sbornik. Mathematics},
     pages = {1693--1705},
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     number = {11},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2000_191_11_a4/}
}
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N. V. Timofeeva. The homology groups of the variety of complete pairs $X_{13}$ of zero-dimensional subschemes of lengths~1 and~3 of projective space. Sbornik. Mathematics, Tome 191 (2000) no. 11, pp. 1693-1705. http://geodesic.mathdoc.fr/item/SM_2000_191_11_a4/