Singular tuples of matrices is not a null cone (and the symmetries of algebraic varieties)
Singular tuples of matrices is not a null cone (and the symmetries of algebraic varieties)
Abstract The following multi-determinantal algebraic variety plays a central role in algebra, algebraic geometry and computational complexity theory: <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mi>SING</m:mi> <m:mrow> <m:mi>n</m:mi> <m:mo>,</m:mo> <m:mi>m</m:mi> </m:mrow> </m:msub> </m:math> {{\rm SING}_{n,m}} , consisting of all m -tuples of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>n</m:mi> <m:mo>×</m:mo> <m:mi>n</m:mi> </m:mrow> </m:math> {n\times n} complex matrices …