Related papers: Numerical Ricci-flat metrics on K3

We review briefly the characteristic topological data of Calabi--Yau threefolds and focus on the question of when two threefolds are equivalent through related topological data. This provides an interesting test case for machine learning…

In a recent paper Donaldson explains how to use an older construction of Joyce to obtain four dimensional local models for scalar-flat Kahler metrics with a 2-torus symmetry. Using this idea, he recovers and generalizes the Taub-NUT metric…

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,…

We prove that Calabi-Yau metrics on compact Calabi-Yau manifolds whose Kahler classes shrink the fibers of a holomorphic fibration have a priori estimates of all orders away from the singular fibers. To this end we prove an asymptotic…

We present an inductive algebraic approach to the systematic construction and classification of generalized Calabi-Yau (CY) manifolds in different numbers of complex dimensions, based on Batyrev's formulation of CY manifolds as toric…

We study unbounded 2-dimensional metric polytopes such as those arising as K\"ahler quotients of complete K\"ahler 4-manifolds with two commuting symmetries and zero scalar curvature. Under a mild closedness condition, we obtain a complete…

A new class of Riemannian metrics, called octonionic K\"ahler, is introduced and studied on a certain class of 16-dimensional manifolds. It is an octonionic analogue of K\"ahler metrics on complex manifolds and of HKT-metrics of…

We focus on the classical open problem of the classification of K\"ahler-Einstein manifolds that can be K\"ahler immersed into a complex projective space endowed with the Fubini-Study metric. In particular, we will deal with such problem in…

Indefinite Kaehler solutions of the Einstein equations are studied, and it is almost completely determined which compact complex surfaces admit such metrics.

In this paper we are concerned with the matrix Li-Yau-Hamilton estimates for nonlinear heat equations. Firstly, we derive such estimate on a K\"{a}hler manifold with a fixed K\"{a}hler metric. Then we consider the estimate on K\"{a}hler…

We study sections of a Calabi-Yau threefold fibered over a curve by K3 surfaces. We show that there exist infinitely many isolated sections on certain K3 fibered Calabi-Yau threefolds and the subgroup of the N\'eron-Severi group generated…

The aim of this paper is to analyze some geometric properties of the rigid Calabi--Yau threefold $\mathcal{Z}$ obtained by a quotient of $E^3$, where $E$ is a specific elliptic curve. We describe the cohomology of $\mathcal{Z}$ and give a…

We solve for the SO(3)-invariant Kahler-Einstein metric on $\mathbb{P}^2$ with cone singularities along a smooth conic curve using numerical approach. The numerical results show the sharp range of angles ($(\pi/2,2\pi]$) for the solvability…

We introduce a large class of canonical K\"ahler metrics, called in this paper well-behaved, extending metrics induced by complex space forms. We study K\"ahler--Ricci iterations of well-behaved metrics on compact and non-compact K\"ahler…

A Calabi-Yau threefold is called of type K if it admits an \'etale Galois covering by the product of a K3 surface and an elliptic curve. In our previous paper, based on Oguiso-Sakurai's fundamental work, we provide the full classification…

We present three families of exact, cohomogeneity-one Einstein metrics in $(2n+2)$ dimensions, which are generalizations of the Stenzel construction of Ricci-flat metrics to those with a positive cosmological constant. The first family of…

This work proves certain general orbifold compactness results for spaces of Riemannian metrics, generalizing earlier results along these lines for Einstein metrics or metrics with bounded Ricci curvature. This is then applied to prove such…

Using numerical methods for finding Ricci-flat metrics, we explore the spectrum of local operators in two-dimensional conformal field theories defined by sigma models on Calabi-Yau targets at large volume. Focusing on the examples of K3 and…

Let $M$ be a complete Ricci-flat Kahler manifold with one end and assume that this end converges at an exponential rate to $[0,\infty) \times X$ for some compact connected Ricci-flat manifold $X$. We begin by proving general structure…

We prove the general diagram method theorem valid for the quite large class of 3-folds with Q-factorial singularities (see Basic Theorem 1.3.2 and also Theorem 2.2.6). This gives the generalization of our results about Fano 3-folds with…