A new Gorenstein format

The construction of projective varieties in Algebraic Geometry using graded rings is hindered by the absence of general structure theorems for homogeneous ideals in codimension greater than or equal to 4. In this talk we explain some new results obtained by joint work with Papadakis. We describe a new format of Gorenstein ideals, in arbitrary codimension, drawn from Reid's serial Kustin-Miller unprojection of a hypersurface ring, and apply it to the construction of numerical Campedelli surfaces with Z/6 torsion.