The most general version of Serre duality states that on certain schemes of dimension , including all projective varieties over any algebraically closed field , there is a natural perfect pairing (http://planetmath.org/BilinearMap)
In special cases, this reduces to more approachable forms. If is nonsingular (or more generally, Cohen-Macaulay), then is simply , where is the sheaf of differentials on .
If is locally free, then
so that we obtain the somewhat more familiar looking fact that there is a perfect pairing .
|Date of creation||2013-03-22 13:51:24|
|Last modified on||2013-03-22 13:51:24|
|Last modified by||mps (409)|