Abstract
We prove that the varieties \(X_{d_1 d_2 } \) of complete pairs of zero-dimensional subschemes of lengths d 1≥ 2, d 2≥ 4 on a smooth irreducible projective algebraic surface are singular.
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REFERENCES
A. S. Tikhomirov, “Variety of complete pairs of zero-dimensional subschemes of an algebraic surface,” Izv. Ross. Akad. Nauk Ser. Mat. [Russian Acad. Sci. Izv. Math.], 61 (1997), no. 6, 153–180.
N. V. Timofeeva, “Smoothness and the Euler characteristic of the variety of complete pairs X 23 of zero-dimensional subschemes of lengths 2 and 3 of an algebraic surface,” Mat. Zametki [Math. Notes], 67 (2000), no. 2, 276–287.
J. Briangon, “Description de Hilbn ℂ{x, y},” Invent. Math,, 41 (1977), 45–89.
D. Mumford, Lectures on Curves on Algebraic Surface, Princeton University Press, Princeton, 1966.
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Timofeeva, N.V. Varieties of Complete Pairs of Zero-Dimensional Subschemes of Lengths ≥2 and ≥4 in Algebraic Surfaces. Mathematical Notes 73, 697–705 (2003). https://doi.org/10.1023/A:1024068923065
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DOI: https://doi.org/10.1023/A:1024068923065