Related papers: Cyclic coverings, Calabi-Yau manifolds and Complex…
We undertake a systematic scan of vector bundles over spaces from the largest database of known Calabi-Yau three-folds, in the context of heterotic string compactification. Specifically, we construct positive rank five monad bundles over…
We construct elements in the motivic cohomology of certain rank 4 weight 3 Calabi--Yau motives, and write down explicit expressions for the regulators of these elements in the context of conjectures on $L$-values such as those of Beilinson…
We show that the Calabi-Yau metrics with isolated conical singularities of Hein-Sun admit polyhomogeneous expansions near their singularities. Moreover, we show that, under certain generic assumptions, natural families of smooth Calabi-Yau…
We provide a set of tools for analyzing the geometry of elliptically fibered Calabi-Yau manifolds, starting with a description of the total space rather than with a Weierstrass model or a specified type of fiber/base. Such an approach to…
We study Calabi-Yau threefolds fibered by abelian surfaces, in particular, their arithmetic properties, e.g., N\'eron models and Zariski density.
We carry out a gluing construction for collapsing warped-QAC (quasi-asymptotically-conical) Calabi-Yau manifolds in $\CC^{n+2}, n\geq 2$. This gluing theorem verifies a conjecture by Yang Li in \cite{li2019gluing} on the behavior of the…
We develop a theory of complex Kuranishi structures on projective schemes. These are sufficiently rigid to be equivalent to weak perfect obstruction theories, but sufficiently flexible to admit global complex Kuranishi charts. We apply the…
As a generalization of a Calabi-Yau category, we will say a k-linear Hom-finite triangulated category is fractionally Calabi-Yau if it admits a Serre functor S and there is an n > 0 with S^n = [m]. An abelian category will be called…
We carry out a systematic analysis of Calabi-Yau threefolds that are elliptically fibered with section ("EFS") and have a large Hodge number h^{2, 1}. EFS Calabi-Yau threefolds live in a single connected space, with regions of moduli space…
We investigate Calabi--Yau three folds which are small resolutions of fiber products of elliptic surfaces with section admitting reduced fibers. We start by the classification of all fibers that can appear on such varieties. Then, we find…
Multiply-connected Calabi-Yau threefolds are of particular interest for both string theorists and mathematicians. Recently it was pointed out that one of the generic degenerations of these spaces (occurring at codimension one in moduli…
In this paper, we study the analogue of the Shafarevich conjecture for polarized Calabi-Yau varieties. We use variations of Hodge structures and Higgs bundles to establish a criterion for the {\it rigidity} of families. We then apply the…
Recent results on duality between string theories and connectedness of their moduli spaces seem to go a long way toward establishing the uniqueness of an underlying theory. For the large class of Calabi-Yau 3-folds that can be embedded as…
This is the second in a series of papers constructing explicit examples of special Lagrangian submanifolds in C^m. The first paper was math.DG/0008021, which studied special Lagrangian m-folds with large symmetry groups. The third is…
The theory of coverings of the two-dimensional torus is a standard part of algebraic topology and has applications in several topics in string theory, for example, in topological strings. This paper initiates applications of this theory to…
We give an explicit example of log Calabi-Yau pairs that are log canonical and have a linearly decreasing Euler characteristic. This is constructed in terms of a degree two covering of a sequence of blow ups of three dimensional projective…
The first part of this paper is a review of the Strominger-Yau-Zaslow conjecture in various settings. In particular, we summarize how, given a pair (X,D) consisting of a Kahler manifold and an anticanonical divisor, families of special…
In this paper, we will construct new examples of derived equivalent Calabi--Yau 3-folds with Picard number greater than one. We also study their mirror Calabi--Yau manifolds and find that they are given by Schoen's fiber products of…
Even a cursory inspection of the Hodge plot associated with Calabi-Yau threefolds that are hypersurfaces in toric varieties reveals striking structures. These patterns correspond to webs of elliptic-K3 fibrations whose mirror images are…
We show how Calabi-Yau hypersurface families arising from Batyrev's construction can be resolved and compactified using a type of fan more general than an MPCP resolution. This can lead to smooth projective compactifications that are not…