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 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 Spec R to be contracted.