Related papers: Calabi problem for manifolds with edge-cone singul…

Motivated by the Strominger-Yau-Zaslow conjecture, we study fibre spaces whose total space has trivial canonical bundle. Especially, we are interest in Calabi-Yau varieties with fibre structure. In this paper, we only consider semi-stable…

The Aluffi algebra is algebraic definition of characteristic cycles of a hypersurface in intersection theory. In this paper we focus on the Aluffi algebra of quasi-homogeneous and locally Eulerian hypersurface with isolated singularities.…

We describe pretty examples of derived equivalences and autoequivalences of Calabi-Yau threefolds arising from pencils of cubic fourfolds. The cubic fourfolds are chosen to be special, so they have an associated K3 surface. Thus a pencil…

We study first order deformations of the tangent sheaf of resolutions of Calabi-Yau threefolds that are of the form $\mathbb{C}^3/Z_r$, focusing on the cases where the orbifold has an isolated singularity. We prove a lower bound on the…

In this paper, we study boundedness questions for (simply-connected) smooth Calabi-Yau threefolds. The diffeomorphism class of such a threefold is known to be determined up to finitely many possibilities by the integral middle cohomology…

We construct a surprisingly large class of new Calabi-Yau 3-folds $X$ with small Picard numbers and propose a construction of their mirrors $X^*$ using smoothings of toric hypersurfaces with conifold singularities. These new examples are…

In many large-scale inverse problems, such as computed tomography and image deblurring, characterization of sharp edges in the solution is desired. Within the Bayesian approach to inverse problems, edge-preservation is often achieved using…

We use the latest techniques in machine-learning to study whether from the landscape of Calabi-Yau manifolds one can distinguish elliptically fibred ones. Using the dataset of complete intersections in products of projective spaces (CICY3…

A compact complex manifold is Kobayashi non-hyperbolic if there exists an entire curve on it. Using mirror symmetry we establish that there are (possibly singular) elliptic or rational curves on any Calabi-Yau manifold $X$, whose mirror…

We study the Gepner model description of D-branes in Calabi-Yau manifolds with singular curves. From a geometrical point of view, the resolution of singularities leads to additional homology cycles around which branes can wrap. Using…

Let M be a compact Riemannian manifold and E a Riemannian vector bundle on M. We look for hypersurfaces of E with a prescribed vertical Gaussian curvature. In trying to solve this problem fibre-wise, we loose the regularity of the resulting…

We use the resolution procedure of Esole and Yau arXiv:1107.0733 to study Yukawa couplings, G-flux, and the emergence of spectral covers from elliptically fibered Calabi-Yau's with a surface of A_4 singularities. We provide a global…

We show that every connected compact or bordered Riemann surface contains a Cantor set whose complement admits a complete conformal minimal immersion in $\mathbb R^3$ with bounded image. The analogous result holds for holomorphic immersions…

In this paper, we investigate the prescribed curvature problem associated with a special Lin-Lu-Yau curvature on finite graphs of girth at least 6. We define the corresponding Calabi flow for this curvature type, and establish an equivalent…

The global characteristic initial value problem for linear wave equations on globally hyperbolic Lorentzian manifolds is examined, for a class of smooth initial value hypersurfaces satisfying favourable global properties. First it is shown…

This is an outline of work in progress concerning an algebro-geometric form of the Strominger-Yau-Zaslow conjecture. We introduce a limited type of degeneration of Calabi-Yau manifolds, which we call toric degenerations. For these, the…

We study super Yang-Mills theories on five-dimensional Sasaki-Einstein manifolds. Using localisation techniques, we find that the contribution from the vector multiplet to the perturbative partition function can be calculated by counting…

On an affine flat manifold with coordinates x^j and convex local potential function f, we call the affine Kahler metric f_{ij} dx^i dx^j semi-flat Calabi-Yau if it satisfies det f_{ij} = 1. Recently Gross-Wilson have constructed many such…

Calabi-Yau manifolds are important objects in algebraic geometry and in theoretical physics. A hypothesis of mirror symmetry is that Calabi-Yau manifolds of dimension 3 come in pairs, with the Hodge numbers of one manifold mirroring the…

Calabi-Yau algebras are particularly symmetric differential graded algebras. There is a construction called `Calabi-Yau completion' which produces a canonical Calabi-Yau algebra from any homologically smooth dg algebra. Homologically smooth…