Quotients of the Dwork pencil

In this paper we investigate the geometry of the Dwork pencil in any dimension. More specifically, we study the automorphism group G of the generic fiber of the pencil over the complex projective line, and the quotients of it by various subgroups of G. In particular, we compute the Hodge numbers of these quotients via orbifold cohomology

Evaluation of the damages caused by lightning current flowing through bearings

A laboratory for lightning current tests was set up allowing the generation of the lightning currents foreseen by the Standards. Lightning tests are carried out on different objects, aircraft materials and components, evaluating the direct and indirect effects of lightning. Recently a research was carried out to evaluate the effects of the lightning current flow through bearings with special reference to wind power generator applications. For this purpose, lightning currents of different amplitude were applied to bearings in different test conditions and the damages caused by the lightning current flow were analyzed. The influence of the load acting on the bearing, the presence of lubricant and the bearing rotation were studied

Hodge numbers for the cohomology of Calabi-Yau type local systems

We use Higgs cohomology to determine the Hodge numbers of the first intersection cohomology group of a local system V arising from the third direct image of a family of Calabi-Yau 3-folds over a smooth, quasi-projective curve. We give applications to Rhode's families of Calabi-Yau 3-folds without MUM.Comment: Some signs corrected. This article draws heavily from arXiv:0911.027

Smooth double covers of K3 surfaces

In this paper we classify the topological invariants of the possible branch loci of a smooth double cover f : X \u2192 Y of a K3 surface Y . We describe some geometric properties of X which depend on the properties of the branch locus. We give explicit examples of surfaces X with Kodaira dimension 1 and 2 obtained as double cover of K3 surfaces and we describe some of them as bidouble cover of rational surfaces. Then, we classify the K3 surfaces which admit smooth double covers X satisfying certain conditions; under these conditions the surface X is of general type, h^{1,0}(X)=0 and h^{2,0}(X)=2. We discuss the variation of the Hodge structure of H^2(X, Z) for some of these surfaces X

Calabi-Yau 3-folds of Borcea-Voisin type and elliptic fibrations

We consider Calabi-Yau 3-folds of Borcea-Voisin type, i.e. Calabi-Yau 3-folds obtained as crepant resolutions of a quotient (5 7 E)/(\u3b1S 7 \u3b1E), where S is a K3 surface, E is an elliptic curve, \u3b1S 08 Aut(S) and \u3b1E 08 Aut(E) act on the period of S and E respectively with order n = 2,3,4,6. The case n = 2 is very classical, the case n = 3 was recently studied by Rohde, the other cases are less known. First, we construct explicitly a cr\ueapant resolution, X, of (S 7 E)/(\u3b1S 7 \u3b1E) and we compute its Hodge numbers; some pairs of Hodge numbers we found are new. Then, we discuss the presence of maximal automorphisms and of a point with maximal unipotent monodromy for the family of X. Finally, we describe the map \u3f5n: X \u2192 S/\u3b1S whose generic fiber is isomorphic to E

Generalized Borcea-Voisin Construction

C. Voisin and C. Borcea have constructed mirror pairs of families of Calabi-Yau threefolds by taking the quotient of the product of an elliptic curve with a K3 surface endowed with a non-symplectic involution. In this paper, we generalize the construction of Borcea and Voisin to any prime order and build three and four dimensional Calabi-Yau orbifolds. We classify the topological types that are obtained and show that, in dimension 4, orbifolds built with an involution admit a crepant resolution and come in topological mirror pairs. We show that for odd primes, there are generically no minimal resolutions and the mirror pairing is lost.Comment: 15 pages, 2 figures. v2: typos corrected & references adde

On certain isogenies between K3 surfaces

We will prove that there are infinitely many families of K3 surfaces which both admit a finite symplectic automorphism and are (desingularizations of) quotients of other K3 surfaces by a symplectic automorphism. These families have an unexpectedly high dimension. We apply this result to construct ``special'' isogenies between K3 surfaces which are not Galois covers between K3 surfaces but are obtained by composing cyclic Galois covers. In the case of involutions, for any nin mathbb{N}_{>0} we determine the transcendental lattices of the K3 surfaces which are $2^n:1$ isogenous (by the mentioned ``special'' isogeny) to other K3 surfaces

Generalized Shioda–Inose structures of order 3

A Shioda–Inose structure is a geometric construction which associates to an Abelian surface a projective K3 surface in such a way that their transcendental lattices are isometric. This geometric construction was described by Morrison by considering special symplectic involutions on the K3 surfaces. After Morrison several authors provided explicit examples. The aim of this paper is to generalize Morrison’s results and some of the known examples to an analogous geometric construction involving not involutions, but order 3 automorphisms. Therefore, we define generalized Shioda–Inose structures of order 3, we identify the K3 surfaces and the Abelian surfaces which appear in these structures and we provide explicit examples

Calabi-Yau 4-folds of Borcea-Voisin type from F-theory

We apply Borcea-Voisin's construction and give new examples of Calabi- Yau 4-folds Y, which admit an elliptic fibration onto a smooth 3-fold V, whose singular fibers of type I5 lie above a del Pezzo surface dP 82 V. These are relevant models for F-theory according to Beasley et al. (2009a, 2009b). Moreover, we give the explicit equations of some of these Calabi-Yau 4-folds and their fibrations