Determinantenring/Charakteristik 0/Differentielle Signatur/Fakt/en

Let ${}K$ be an algebraically closed field of characteristic zero.

Then the differential signature of the determinantal ring of ${}m\times n$-matrices of rank ${}r$

${}R=K[X_{a,b},\,1\leq a\leq m,\,1\leq b\leq n]/({\text{ minors of seize }}r)\,$

is

${\frac {1}{2^{r(m+n-r)}}}\det {\left({\binom {m+n-i-j}{m-i}}_{1\leq i,j\leq r}\right)}.$