Variety of Orthogonal Frames Analysis
Published:Dec 31, 2025 18:53
•1 min read
•ArXiv
Analysis
This paper explores the algebraic variety formed by orthogonal frames, providing classifications, criteria for ideal properties (prime, complete intersection), and conditions for normality and factoriality. The research contributes to understanding the geometric structure of orthogonal vectors and has applications in related areas like Lovász-Saks-Schrijver ideals. The paper's significance lies in its mathematical rigor and its potential impact on related fields.
Key Takeaways
- •Investigates the algebraic variety of orthogonal frames.
- •Provides classifications and criteria for key properties of the variety and associated ideal.
- •Offers applications to the theory of Lovász-Saks-Schrijver ideals.
Reference
“The paper classifies the irreducible components of V(d,n), gives criteria for the ideal I(d,n) to be prime or a complete intersection, and for the variety V(d,n) to be normal. It also gives near-equivalent conditions for V(d,n) to be factorial.”