Quadrik/Charakteristik 0/Differentielle Signatur/Fakt/en

Let ${}K$ be an algebraically closed field of characteristic zero and ${}d\geq 2$.

Then the differential signature of the quadric hypersurface

${}R=K[X_{1},\ldots ,X_{d+1}]/{\left(X_{1}^{2}+\cdots +X_{d+1}^{2}\right)}\,$

is ${}{\left({\frac {1}{2}}\right)}^{d-1}$.