The homology groups of the variety of complete pairs $X_{13}$ of zero-dimensional subschemes of lengths 1 and 3 of projective space

N. V. Timofeeva

Yaroslavl State Pedagogical University named after K. D. Ushinsky

Abstract: 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.

UDC: 517.2

MSC: Primary 14C05; Secondary 14C15

Received: 11.06.1999 and 24.01.2000

DOI: 10.4213/sm523

 English version: Sbornik: Mathematics, 2000, 191:11, 1693–1705

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