Structure theorems for certain Gorenstein ideals
Juan Elias, Giuseppe Valla
TL;DR
This paper establishes a structure theorem for a specific class of Artinian Gorenstein local rings, explores their moduli, and provides bounds on generators of perfect ideals.
Contribution
It introduces a new structure theorem for Gorenstein ideals with squared maximal ideal generated by two elements and discusses related moduli problems.
Findings
Provides a classification for certain Gorenstein local rings.
Discusses the moduli space of these algebras.
Establishes bounds on the minimal number of generators for perfect ideals.
Abstract
The main achievement of this paper is to provide a structure theorem for Artinian, Gorenstein local rings with the property that the square of the maximal ideal is generated by two elements. The moduli problem for this class of local algebras is also discussed. Finally, upper and lower bounds for the minimal number of generators of perfect ideals are given.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic Geometry and Number Theory · Algebraic structures and combinatorial models