Let K {\displaystyle {}K} be an algebraically closed field of characteristic zero. Let f {\displaystyle {}f} be an irreducible quadric in d + 1 {\displaystyle {}d+1} variables, d ≥ 2 {\displaystyle {}d\geq 2} .
Then the symmetric powers Sym n ( Syz ( x 1 , … , x d + 1 ) ) ( m ) {\displaystyle {}\operatorname {Sym} ^{n}(\operatorname {Syz} (x_{1},\ldots ,x_{d+1}))(m)} on the quadric
have no nontrivial section for m < 3 2 n {\displaystyle {}m<{\frac {3}{2}}n} .
be an algebraically closed field of characteristic zero. Let 
be an irreducible quadric in 
variables,
.
on the quadric
![{\displaystyle {}Q_{d}=\operatorname {Proj} K[x_{1},\ldots ,x_{d+1}]/(f)\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c899633e2f749c6c154544f5d1e7b4bfa81d8093)
.
