Room P3.10, Mathematics Building

Stavros Papadakis, Instituto Superior Técnico
Parallel unprojection of type Kustin-Miller

Unprojection theory, initiated by Miles Reid, aims to construct and analyze complicated commutative rings in terms of simpler ones. The unprojection of type Kustin-Miller is the simplest type of unprojection. It is specified by the data of a Gorenstein local ring $R$ and a codimension $1$ ideal $I$ with the quotient ring $R/I$ being Gorenstein, and constructs a new Gorenstein ring $S$, which geometrically corresponds to the birational contraction of the closed subscheme $V(I)$ of $\operatorname{Spec} R$. The talk will be about recent joint work with Jorge Neves (Coimbra) concerning the parallel unprojection of type Kustin-Miller, which is a generalization corresponding to the case where there are more than one Gorenstein subschemes of $\operatorname{Spec} R$ to be contracted.