Depth of powers of edge ideals of edge-weighted integrally closed cycles

Key Points

• The aim is to compute the depth of powers of edge ideals specifically for edge-weighted integrally closed cycles.
• Analyzed edge ideals associated with integrally closed cycles.
• Computed their depths through algebraic methods.
• Explored properties of edge-weighted structures in cycles.
• Identified specific patterns in the depth of the powers of edge ideals.
• Highlighted differences in behavior compared to traditional edge ideals.
• Provided insights into the implications for algebraic geometry.