Stavros Argyrios Papadakis

A CONSTRUCTION OF NUMERICAL CAMPEDELLI SURFACES WITH TORSION Z/6

We produce a family of numerical Campedelli surfaces with Z/6 torsion by constructing the canonical ring of the etale 6 to 1 cover using serial unprojection. In Section 2 we develop the necessary algebraic machinery. Section 3 contains the numerical Campedelli surface construction, while Section 4 contains remarks and open questions.

Parallel Kustin-Miller unprojection with an application to Calabi-Yau geometry

Kustin--Miller unprojection constructs more complicated Gorenstein rings from simpler ones. Geometrically, it inverts certain projections, and appears in the constructions of explicit birational geometry. However, it is often desirable to perform not only one but a series of unprojections. The main aim of the present paper is to develop a theory, which we call parallel Kustin--Miller unprojection, that applies when all the unprojection ideals of a series of unprojections correspond to ideals already present in the initial ring. As an application of the theory, we explicitly construct 7 families of Calabi--Yau 3-folds of high codimensions.