Twisted tensor products of K3 with K3

K3 K3 K3 Surfaces with Involution and Analytic Torsion

In a series of works [Bo3-5], Borcherds developed a theory of modular forms over domains of type IV which admits an infinite product expansion. Such modular forms are said to be Borcherds's product in this paper. Among all Borcherds's products, Borcherds's Φ-function ([Bo4]) has an interesting geometric background; It is a modular form on the moduli space of Enriques surfaces characterizing the...

Metric packing for K3+K3

Mirrorfolds with K3 Fibrations

We study a class of non-geometric string vacua realized as completely soluble superconformal field theory (SCFT). These models are defined as ‘interpolating orbifolds’ of K3×S1 by the mirror transformation acting on the K3 fiber combined with the half-shift on the S1-base. They are variants of the T-folds, the interpolating orbifolds by T-duality transformations, and thus may be called ‘mirrorf...

Cohomology of Twisted Tensor Products

It is well known that the cohomology of a tensor product is essentially the tensor product of the cohomologies. We look at twisted tensor products, and investigate to which extent this is still true. We give an explicit description of the Ext-algebra of the tensor product of two modules, and under certain additional conditions, describe an essential part of the Hochschild cohomology ring of a t...

K3 Surfaces with Nine Cusps

By a K3-surface with nine cusps I mean a surface with nine isolated double points A 2 , but otherwise smooth, such that its minimal desingularisation is a K3-surface. It is shown, that such a surface admits a cyclic triple cover branched precisely over the cusps. This parallels the theorem of Nikulin, that a K3-surface with 16 nodes is a Kummer quotient of a complex torus.