Related papers: Mabuchi and Aubin-Yau functionals over complex thr…
This paper is a follow-up to an earlier paper math.DG/0410260 on desingularizations of Calabi-Yau 3-folds with a conical singularity. In math.DG/0410260 we study Calabi-Yau 3-folds M_0 with a conical singularity at x modelled on some…
We discuss aspects of the algebraic geometry of compact non-commutative Calabi-Yau manifolds. In this setting, it is appropriate to consider local holomorphic algebras which can be glued together into a compact Calabi-Yau algebra. We…
We give a new example of a compact manifold with holonomy Spin(7) from a Beauville's Calabi-Yau fourfold. Its construction is very concrete, starting with products of elliptic curves with complex multiplications --- so probably more…
In this paper we construct explicit smooth solutions to the Strominger system on generalized Calabi-Gray manifolds, which are compact non-K\"ahler Calabi-Yau 3-folds with infinitely many distinct topological types and sets of Hodge numbers.
We study compactifications of eleven- and ten-dimensional maximal supergravity on Calabi-Yau threefolds. We explicitly construct truncations to pure supergravity with eight supercharges in five and four dimensions and show that they are…
We consider Calabi-Yau compactifications with one K\"ahler modulus. Following the method of Candelas et al. we use the mirror hypothesis to solve the quantum theory exactly in dependence of this modulus by performing the calculation for the…
In this paper we explore contributions to non-perturbative superpotentials arising from instantons wrapping effective divisors in smooth Calabi-Yau four-folds. We concentrate on the case of manifolds constructed as complete intersections in…
Any Calabi-Yau threefold X with infinite fundamental group admits an \'etale Galois covering either by an abelian threefold or by the product of a K3 surface and an elliptic curve. We call X of type A in the former case and of type K in the…
This article first reviews the calculation of the N = 1 effective action for generic type IIA and type IIB Calabi-Yau orientifolds in the presence of background fluxes by using a Kaluza-Klein reduction. The Kahler potential, the gauge…
We describe birational models and decide the rationality/unirationality of moduli spaces AA_{d} (and AA^{lev}_{d}) of (1,d)-polarized abelian surfaces (with canonical level structure, respectively) for small values of d. The projective…
The special geometries of two recently discovered Calabi-Yau threefolds with $h^{11}=1$ are analyzed in detail. These correspond to the 'minimal three-generation' manifolds with $h^{21}=4$ and the `24-cell' threefolds with $h^{21}=1$. It…
A numerical algorithm for explicitly computing the spectrum of the Laplace-Beltrami operator on Calabi-Yau threefolds is presented. The requisite Ricci-flat metrics are calculated using a method introduced in previous papers. To illustrate…
We study threefolds fibred by mirror quartic K3 surfaces. We begin by showing that any family of such K3 surfaces is completely determined by a map from the base of the family to the moduli space of mirror quartic K3 surfaces. This is then…
The four-dimensional effective theory for type IIB warped flux compactifications proposed in [1] is completed by taking into account the backreaction of the K\"ahler moduli on the three-form fluxes. The only required modification consists…
We call a projective Calabi-Yau (CY) 3-fold almost generic if it has only isolated nodes as singularities and the homology classes of all of the exceptional curves in an analytic small resolution are non-trivial but torsion. Such a…
We establish plurisubharmonicity of the envelope of Poisson and Lelong functionals on almost complex manifolds. That is, we generalize the corresponding results for complex manifolds and almost complex manifolds of complex dimension two. We…
We describe bivector fields and Poisson structures on local Calabi-Yau threefolds which are total spaces of vector bundles on a contractible rational curve. In particular, we calculate all possible holomorphic Poisson structures on the…
We complete the classification (started by Bray and the second author) of all closed 3-manifolds with Yamabe invariant greater than that of $\RP^3$, by showing that such manifolds are either $S^3$ or finite connected sums $# m(S^2 \times…
We construct new complete Calabi-Yau metrics on the complement of an anticanonical divisors $D$ in a Fano manifold of dimension at least three, when $D$ consists of two transversely intersecting smooth divisors. The asymptotic geometry is…
The aim of the paper is to investigate the only two families $\mathcal{F}^A_{G}$ of Calabi-Yau $3$-folds $A/G$ with $A$ an abelian $3$-fold and $G\le \text{Aut}(A)$ a finite group acting freely: one in constructed by Catanese and Demleitner…