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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb., 2003 Volume 194, Number 3, Pages 53–60 (Mi sm720)

The variety of complete pairs of zero-dimensional subschemes of length 2 of a smooth three-dimensional variety is singular

N. V. Timofeeva

Yaroslavl State Pedagogical University named after K. D. Ushinsky

Abstract: Equations are obtained that are satisfied by the vectors of the tangent space to the variety $X_{22}$ of complete pairs of zero-dimensional subschemes of length 2 of a smooth three-dimensional projective algebraic variety at the most special point of the variety $X_{22}$. It is proved that the system of equations obtained is complete and the variety $X_{22}$ is singular.

UDC: 517.2

MSC: Primary 14C05; Secondary 14B05, 14B10

Received: 25.01.2002 and 17.07.2002

DOI: 10.4213/sm720


 English version:
Sbornik: Mathematics, 2003, 194:3, 361–368

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