Related papers: On Complex Supermanifolds with Trivial Canonical B…

We survey mirror symmetry of Calabi-Yau manifolds from the perspective of families of Calabi-Yau manifolds and their period integrals. Special emphasis is laid on distinguished properties of the hypergeometric series of Gel'fand, Kapranov,…

In this paper we partly extend the Beauville-Bogomolov decomposition theorem to the singular setting. We show that any complex projective variety of dimension at most five with canonical singularities and numerically trivial canonical class…

Consider a smooth, projective family of canonically polarized varieties over a smooth, quasi-projective base manifold Y, all defined over the complex numbers. It has been conjectured that the family is necessarily isotrivial if Y is special…

We study rank $1$ flat bundles over solvmanifolds whose cohomologies are non-trivial. By using Hodge theoretical properties for all topologically trivial rank $1$ flat bundles, we represent the structure theorem of K\"ahler solvmanifolds as…

We use hyperbolic geometry to construct simply-connected symplectic or complex manifolds with trivial canonical bundle and with no compatible Kahler structure. We start with the desingularisations of the quadric cone in C^4: the smoothing…

We prove that the canonical bundle of any holomorphic family of compact complex algebraic manifolds carries a singular Hermitian metric having non-negative curvature current and such that every holomorphic section of the canonical bundle of…

We consider a generalization of Calabi-Yau structures in the context of $\alpha$-Sasakian manifolds. We study deformations of a special class of Legendrian submanifolds and classify invariant contact Calabi-Yau structures on 5-dimensional…

We prove that any holomorphic vector bundle admitting a holomorphic connection, over a compact K\"ahler Calabi-Yau manifold, also admits a flat holomorphic connection. This addresses a particular case of a question asked by Atiyah and…

We show how to construct supersymmetric three-generation models with gauge group and matter content of the Standard Model in the framework of non-simply-connected elliptically fibered Calabi-Yau manifolds Z. The elliptic fibration on a…

Recent results on duality between string theories and connectedness of their moduli spaces seem to go a long way toward establishing the uniqueness of an underlying theory. For the large class of Calabi-Yau 3-folds that can be embedded as…

We determine the Batalin-Vilkovisky Lie algebra structure for the integral loop homology of special unitary groups and complex Stiefel manifolds. It is shown to coincide with the Poisson algebra structure associated to a certain odd…

We apply our earlier work on the higher-dimensional analogue of the Mumford conjecture to two questions. Inspired by work of Ebert we prove non-triviality of certain characteristic classes of bundles of smooth closed manifolds. Inspired by…

In this note, we propose a new approach to solving the Calabi problem on manifolds with edge-cone singularities of prescribed angles along complex hypersurfaces. It is shown how the classical approach of Aubin-Yau in derving {\it a priori}…

In the first part of this paper we consider compact algebraic manifolds M^2n with an algebraic (n-1)-Torus action. We show that there is a T-invariant meromorphic section $\sigma$ of the canonical bundle of M. Any such $\sigma$ defines a…

We show that there exist flat surface bundles with closed leaves having non-trivial normal bundles. This leads us to compute the Abelianisation of surface diffeomorphism groups with marked points. We also extend a formula of Tsuboi that…

We study certain moduli spaces of sheaves on Enriques surfaces thereby obtaining, in every odd dimension, new examples of Calabi-Yau manifolds. We describe the geometry (canonical bundle, fundamental group, second Betti number and certain…

We present closed form expressions for the ranks of all cohomology groups of holomorphic line bundles on several Calabi-Yau threefolds realised as complete intersections in products of projective spaces. The formulae have been obtained by…

A notion known as smooth envelope, or superposition closure, appears naturally in several approaches to generalized smooth manifolds which were proposed in the last decades. Such an operation is indispensable in order to perform…

We review the major mathematical concepts involved in the dimensional reduction of D=11 N=1 supergravity theory over a Calabi-Yau manifold with non-trivial complex structure moduli resulting in ungauged D=5 N=2 supergravity theory with…

In this paper we describe a physical realization of a family of non-compact Kahler threefolds with trivial canonical bundle in hybrid Landau-Ginzburg models, motivated by some recent non-Kahler solutions of Strominger systems, and utilizing…