What type of study is this?

This is a Quantitative Study study.

October 16, 2025Open Access

Syzygies of some invariant rings with cyclic group actions

View Full Paper

Ask AI

Bookmark

The study finds a full classification of invariant rings for cyclic groups, enriching our understanding of polynomial rings.
Key results highlight specific cases where the defining ideal has codimension two and where multidegrees lie on two lines.
The approach utilizes minimal free resolution to analyze polynomial rings under cyclic group actions, revealing significant structures.
This research supports the ongoing development of algebraic methods in understanding invariant rings further.

Implication

This investigation classifies invariant rings under cyclic group actions, indicating distinct cases with codimension two.

Abstract

We investigate actions of cyclic groups on polynomial rings with two variables, and the minimal free resolution of the corresponding invariant ring. In particular, we fully classify several cases, including the case the defining ideal has codimension two, and when the multidegrees of generating invariants lie on the union of two lines.

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

Christin Sum (2025) studied this question.

synapsesocial.com/papers/68f0f51d8dd8ea469b1d7160 https://doi.org/10.48550/arxiv.2508.05879

View Full Paper

Ask AI

Bookmark

Implication

This investigation classifies invariant rings under cyclic group actions, indicating distinct cases with codimension two.

Syzygies of some invariant rings with cyclic group actions

Key Points

Implication

Abstract

Discussion

Cite This Study

Syzygies of some invariant rings with cyclic group actions

Key Points

Implication

Abstract

Discussion

Cite This Study

Keep reading

Keep reading