2008/12/02 by Shaowei Lin, Bernd Sturmfels, Lin, Shaowei +1
Computer Science · Engineering · #13P10 #14L30 #14M12 #15A15 #15A29 #15A72 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Computer and information sciences #FOS: Mathematics #Polynomial and algebraic computation #Symbolic Computation (cs.SC) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.0812.0601
openalex publication_date 2008/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The image of the principal minor map for n x n-matrices is shown to be closed. In the 19th century, Nansen and Muir studied the implicitization problem of finding all relations among principal minors when n=4. We complete their partial results by constructing explicit polynomials of degree 12 that scheme-theoretically define this affine variety and also its projective closure in \PP15. The latter is the main component in the singular locus of the 2 x 2 x 2 x 2-hyperdeterminant.