Varieties of complete pairs of zero-dimensional subschemes of lengths \(\geq 2\) and \(\geq 4\) of an algebraic surface.
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)].
scientific article; zbMATH DE number 2120980