Let K {\displaystyle {}K} be an algebraically closed field of characteristic zero and d ≥ 2 {\displaystyle {}d\geq 2} .
Then the differential signature of the quadric hypersurface
is ( 1 2 ) d − 1 {\displaystyle {}{\left({\frac {1}{2}}\right)}^{d-1}} .
be an algebraically closed field of characteristic zero and
.
![{\displaystyle {}R=K[X_{1},\ldots ,X_{d+1}]/{\left(X_{1}^{2}+\cdots +X_{d+1}^{2}\right)}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a437c80f76dcaff1b3445a0bacd3694231abf4b9)
.
