Related papers: Some ball quotients with a Calabi--Yau model
We find a simple geometric construction of Tonoli's examples of Calabi--Yau threefolds of degree 17 in complex $\mathbb{P}^6$. We prove that the rank of the Picard group of elements of one of these families is at least $2$.
We introduce the notion of K-correspondence, and show that many Calabi-Yau varieties carry a lot of self-K-isocorrespondences, which furthermore satisfy the property of multiplying the canonical volume form by a constant of modulus…
Inspired Yau's work (Comm. Anal. Geom., 1994), in this short note we provide a new version of Li-Yau gradient estimate for the linear heat equation, which generalizes some known results and gives new gradient estimates. Also we explain the…
In this note we initiate a program to obtain global descriptions of Calabi-Yau moduli spaces, to calculate their Picard group, and to identify within that group the Hodge line bundle, and the closely-related Bagger-Witten line bundle. We do…
We study Kustin--Miller unprojections of Calabi--Yau threefolds. As an application we work out the geometric properties of Calabi--Yau threefolds defined as linear sections of determinantal varieties. We compute their Hodge numbers and…
We show an example of a non-archimedean version of the Calabi-Yau theorem in complex geometry. Precisely, we consider totally degenerate abelian varieties and certain probability measures on their associated analytic spaces in the sense of…
We formulate a version of the integral Hodge conjecture for categories, prove the conjecture for two-dimensional Calabi-Yau categories which are suitably deformation equivalent to the derived category of a K3 or abelian surface, and use…
We give an algebraic characterization of Picard-Fuchs operators attached to families of Calabi-Yau manifolds with a point of maximally unipotent monodromy and discuss possibilities for their differential Galois groups.
In this paper we show that the dual complex of a dlt log Calabi-Yau pair $(Y, \Delta)$ on a Mori fibre space $\pi: Y \to Z$ is a finite quotient of a sphere, provided that either the Picard number of $Y$ or the dimension of $Z$ is $\leq 2$.…
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 prove that compact Calabi--Yau varieties with certain isolated singularities are projective. In dimension 3 we do this by analysis, supposing given conifold metrics. In higher dimensions it follows more readily from Ohsawa's degenerate…
We study noncompact Calabi-Yau threefolds, their moduli spaces of vector bundles and deformation theory. We present Calabi-Yau threefolds that have infinitely many distinct deformations, constructing them explicitily, and describe the…
In order to support the odd moduli in models of (type IIB) string compactification, we classify the Calabi-Yau threefolds with h^{1,1}<=4 which exhibit pairs of identical divisors, with different line-bundle charges, mapping to each other…
Call a projective variety $X$ Calabi-Yau if its canonical divisor is ${\bf Q}$-linearly equivalent to zero. The smallest positive integer $m$ with $mK_X$ linearly equivalent to zero is called the index of $X$. We construct Calabi-Yau…
Birational Calabi-Yau threefolds in the same deformation family provide a `weak' counterexample to the global Torelli problem, as long as they are not isomorphic. In this paper, it is shown that deformations of certain desingularized…
This is the author's PhD thesis. Two main sections address various aspects of mirror symmetry for compact Calabi-Yau threefolds and the roles that classically modular varieties play in string theory compactifications. The main results…
We prove that the bounded derived category of the lattice of order ideals of the product of two ordered chains is fractionally Calabi-Yau. We also show that these lattices are derived equivalent to higher Auslander algebras of type A. The…
We study modules over the algebroid stack $\W[\stx]$ of deformation quantization on a complex symplectic manifold $\stx$ and recall some results: construction of an algebra for $\star$-products, existence of (twisted) simple modules along…
The singular cochain complex of a topological space is a classical object. It is a Differential Graded algebra which has been studied intensively with a range of methods, not least within rational homotopy theory. More recently, the tools…
In this paper we introduce a new equation on the compact Kahler manifolds. Solution of this equation corresponds to the Calabi-Yau metric. New equation differs from the Monge--Ampere equation considered by Calabi and Yau.