Syzygies of some invariant rings with cyclic group actions

Key Points

• 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.