Related papers: Numerical Calabi-Yau metrics from holomorphic netw…
We study the collapsing behaviour of Ricci-flat Kahler metrics on a projective Calabi-Yau manifold which admits an abelian fibration, when the volume of the fibers approaches zero. We show that away from the critical locus of the fibration…
With a bird's-eye view, we survey the landscape of Calabi-Yau threefolds, compact and non-compact, smooth and singular. Emphasis will be placed on the algorithms and databases which have been established over the years, and how they have…
Hermitian, pluriclosed metrics with vanishing Bismut-Ricci form give a natural extension of Calabi-Yau metrics to the setting of complex, non-K\"ahler manifolds, and arise independently in mathematical physics. We reinterpret this condition…
We construct all possible complete intersection Calabi-Yau five-folds in a product of four or less complex projective spaces, with up to four constraints. We obtain $27068$ spaces, which are not related by permutations of rows and columns…
We construct new examples of $t$-Gauduchon Ricci-flat metrics, for all $t<1$, on compact non-K\"{a}hler Calabi-Yau manifolds defined by certain principal torus bundles over rational homogeneous varieties with Picard number $\varrho(X) > 1$.…
We propose a class of N=2 supersymmetric nonlinear sigma models on the noncompact Ricci-flat Kahler manifolds, interpreted as the complex line bundles over the hermitian symmetric spaces. Kahler potentials and Ricci-flat metrics for these…
By using the global deformation of almost complex structures which are compatible with a symplectic form off a Lebesgue measure zero subset, we construct a (measurable) Lipschitz Kahler metric such that the one-form type Calabi-Yau equation…
In this work, we describe the asymptotic behavior of complete metrics with prescribed Ricci curvature on open Kahler manifolds that can be compactified by the addition of a smooth and ample divisor. First, we construct a explicit sequence…
The moduli spaces of Calabi--Yau (CY) manifolds are the special K\"ahler manifolds. The special K\"ahler geometry determines the low-energy effective theory which arises in Superstring theory after the compactification on a CY manifold. For…
It is known that moduli spaces of Calabi-Yau (CY) manifolds are special K\"ahler manifolds. This structure determines the corresponding low-energy effective theory which arises in superstring compactifications on CY manifolds. In the case,…
The latest techniques from Neural Networks and Support Vector Machines (SVM) are used to investigate geometric properties of Complete Intersection Calabi-Yau (CICY) threefolds, a class of manifolds that facilitate string model building. An…
Calabi-Yau manifolds can be obtained as hypersurfaces in toric varieties built from reflexive polytopes. We generate reflexive polytopes in various dimensions using a genetic algorithm. As a proof of principle, we demonstrate that our…
We clarify the recently proposed method to compute a Special K\"ahler metric on a Calabi-Yau complex structures moduli space that uses the fact that the moduli space is a subspace of specific Frobenius manifold. We apply this method to…
We present new complete Calabi-Yau metrics defined on the complement of a smooth anticanonical divisor with ample normal bundle, approaching the Calabi model space at a polynomial rate. Moreover, we establish the uniqueness of this type of…
Calabi-Yau manifolds have played a key role in both mathematics and physics, and are particularly important for deriving realistic models of particle physics from string theory. Unfortunately, very little is known about the explicit metrics…
Calabi-Yau links are specific $S^1$-fibrations over Calabi-Yau manifolds, when the link is 7-dimensional they exhibit both Sasakian and G2 structures. In this invited contribution to the DANGER proceedings, previous work exhaustively…
In this manuscript, we demonstrate, using several regression techniques, that the remaining independent Hodge numbers of complete intersection Calabi-Yau four-folds and five-folds can be machine learned from $h^{1,1}$ and $h^{2,1}$.…
Tian and Yau constructed a complete Ricci-flat K\"ahler metric on the complement of an ample and smooth anticanonical divisor. We inquire into the behaviour of this metric towards the boundary divisor and prove a slow decay rate of the…
The hidden symmetries of higher dimensional Kerr-NUT-(A)dS metrics are investigated. In certain scaling limits these metrics are related to the Einstein-Sasaki ones. The complete set of Killing-Yano tensors of the Einstein-Sasaki spaces are…
We present a pedagogical introduction to the recent advances in the computational geometry, physical implications, and data science of Calabi-Yau manifolds. Aimed at the beginning research student and using Calabi-Yau spaces as an exciting…