Characterization of Primary Decomposition of Adjacent Minors of Matrices and Tensors
By: Aswin Rangasamy Venkatesan
Department: Mathematics
Faculty Advisor: Dr. Serkan Hosten
Minimal primes of ideals generated by 2x2 adjacent minors of generic mxn matrix have been previously studied. However, it is still an open problem to characterize the minimal primes of higher dimensional minors. For example, the characterization of the minimal primes of the 3x3 adjacent minors of an mxn matrix is still unknown. In this work, we develop a new approach to characterize them and we also present some computational results. Moreover, we also present a characterization of the minimal primes of the 2x2x..x2 adjacent minors of a 2x2x..xk tensors.