Seminar

We saw in an earlier talk that if $Y$ is a set theoretical complete intersection of codimension $r$ in $\mathbb P^n$, than the local cohomology group $M=H^r_Y(S)$ has codepth $r$. In this talk we show that codepth $\ge 2$ implies that the module $M$ is quasi-principal, meaning any finitely generated submodule is contained in a principal submodule. Then we give some examples and show how this may apply to the rational quartic curve in $\mathbb P^3$.