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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

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