On Rees algebras of ideals and modules over hypersurface rings

2021/12/03 by Weaver, Matthew · 3 citations
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2112.02148

Abstract

The acquisition of the defining equations of Rees algebras is a natural way to study these algebras and allows certain invariants and properties to be deduced. In this paper, we consider Rees algebras of codimension 2 perfect ideals of hypersurface rings and produce a minimal generating set for their defining ideals. Then, using generic Bourbaki ideals, we study Rees algebras of modules with projective dimension one over hypersurface rings. We describe the defining ideal of such algebras and determine Cohen-Macaulayness and other invariants.

Cited by

• On Rees algebras and de Jonquières transformations
• Blowups of hypersurfaces
• Rees algebra and almost linearly presented ideals in three variables

Related

• Cohen-Macaulayness of Rees Algebras of Modules
• On Rees algebras of linearly presented ideals and modules
• The equations of Rees algebras of height three Gorenstein ideals in hypersurface rings
• Cohen-Macaulay fiber cones and defining ideal of Rees algebras of modules
• Blowups of hypersurfaces