Varieties of Complete Pairs of Zero-Dimensional Subschemes of Lengths $\ge2$ and $\ge4$ in Algebraic Surfaces

N. V. Timofeeva

Yaroslavl State Pedagogical University named after K. D. Ushinsky

Abstract: We prove that the varieties $X_{d_1d_2}$ of complete pairs of zero-dimensional subschemes of lengths $d_1\ge2$, $d_2\ge4$ on a smooth irreducible projective algebraic surface are singular.

UDC: 517.2

Received: 27.03.2002

DOI: 10.4213/mzm224

 English version: Mathematical Notes, 2003, 73:5, 697–705

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