Equations of blowups of ideals of codimension two and three
This paper is devoted to the study of the defining equations of blow-up algebras in some particular cases. Blow-up algebras often appear in algebraic geometry and represent fibrations of a variety. More precisely, the author provides a generating set for the equations of Rees algebras of a Cohen-Macaulay domain associated to an ideal \(I\) of codimension two. \(I\) is required to satisfy some additional conditions and the result depends on the parity of the dimension of the base ring. The main aim of section 3 of the paper is to prove this central result. The generating set is given in terms of the jacobian dual of a presentation matrix of \(I\). The jacobian dual of a matrix is introduced and studied in section 2. Finally in section 4, some remarks are given concerning the degrees of the generators of the defining ideal whenever \(I\) is a codimension three Gorenstein ideal.
scientific article; zbMATH DE number 896555
scientific article