Gorenstein Endomorphism Rings on Curve Singularities
Philipp Korell
TL;DR
This paper characterizes when endomorphism rings of fractional ideals on curve singularities are Gorenstein, linking it to ideal stability and semigroup conditions, and classifies Gorenstein algebroid curves with Gorenstein extensions.
Contribution
It introduces criteria for Gorensteinness of endomorphism rings on curve singularities and classifies certain Gorenstein algebroid curves with Gorenstein extensions.
Findings
Gorensteinness characterized by ideal stability and semigroup conditions
Classification of Gorenstein algebroid curves with Gorenstein integral extensions
Criteria applicable to fractional ideals on curve singularities
Abstract
We characterize the Gorensteinness of endomorphism rings of a fractional ideal on a curve singularity by stability of the ideal and a condition on its value semigroup ideal. Moreover, the Gorenstein algebroid curves with only Gorenstein integral extensions are classified.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic Geometry and Number Theory · Algebraic structures and combinatorial models