Varieties of complete pairs of zero-dimensional subschemes of lengths \(\geq 2\) and \(\geq 4\) of an algebraic surface. (Q1889469)
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scientific article; zbMATH DE number 2120980
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Varieties of complete pairs of zero-dimensional subschemes of lengths \(\geq 2\) and \(\geq 4\) of an algebraic surface. |
scientific article; zbMATH DE number 2120980 |
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Varieties of complete pairs of zero-dimensional subschemes of lengths \(\geq 2\) and \(\geq 4\) of an algebraic surface. (English)
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2 December 2004
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This paper deals with certain aspects of the theory of Hilbert schemes of points on algebraic surfaces. The author considers a variety \(X_{d_1 d_2}\) of some special {pairs} \((A_{d_1},A_{d_2})\) of zero-dimensional subschemes of length \((d_1,d_2)\). It is proven that \(X_{23}\) is smooth and \(X_{24}\) is singular, thus disproving a conjecture by \textit{A. S. Tikhomirov} [Izv. Math. 61, No. 6, 1265--1291 (1997; Zbl 0935.14002)].
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