PULLBACK OF THE NORMAL MODULE OF IDEALS WITH LOW CODIMENSION

Author(s)

Miranda-Neto, Cleto B. ^[1]

Affiliation

^[1] Univ Fed Paraiba, BR-58051900 Joao Pessoa, Paraiba - Brazil

• Document type: Journal article
• Source: QUARTERLY JOURNAL OF MATHEMATICS; v. 72, n. 4, p. 1147-1166, DEC 2021.
• Web of Science Citations: 0

Abstract

The normal module (or sheaf) of an ideal is a celebrated object in commutative algebra and algebraic geometry. In this paper, we prove results about its pullback under the natural projection, focusing on subtle numerical invariants such as, for instance, the reduction number. For certain codimension 2 perfect ideals, we show that the pullback has reduction number two. This is of interest since the determination of this invariant in the context of modules (even for special classes) is a mostly open, difficult problem. The analytic spread is also computed. Finally, for codimension 3 Gorenstein ideals, we determine the depth of the pullback, and we also consider a broader class of ideals provided that the Auslander transpose of the conormal module is almost Cohen-Macaulay. (AU)

• FAPESP's process: 19/21843-2 - Local cohomology, homological problems and blowup algebras
• Grantee: Victor Hugo Jorge Pérez
• Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil