Roller coaster curve singularities
Let \(A\) be a 1-dimensional Cohen-Macaulay local ring; the Hilbert function \(H_ A\) is said to have \(n\) valleys if there are integers \(2\leq a_ 1\leq\dots \leq a_ n\) such that (for \(i=1,\dots, n\)) \(H_ A(a_ i-1)> H_ A(a_ i)\) and \(H_ A(a_ i)< H_ A(a_ i+1)\). In the literature there are examples of locally decreasing Hilbert functions with one valley. In this paper the author, starting from a construction of \textit{L. G. Roberts} [Can. J. Math. 34, 169-180 (1982; Zbl 0439.14007)], gives examples of ordinary curve singularities with an arbitrary large number of valleys.
scientific article; zbMATH DE number 645111