Projective complete intersection
= Projective complete intersection
A projective complete intersection is a <closed subscheme> of a <projective space> defined by a homogeneous <regular sequence> of positive degrees. A length-$r$ sequence in $k[t_0,\ldots,t_N]$ gives dimension $N-r$ when $r\le N$. Sheafifying its successive quotient sequences gives exact restriction sequences of <twisting sheaves on projective space>, allowing computation of its <sheaf cohomology>. It need not be smooth or reduced.