Related papers: Calabi--Yau threefolds in $\mathbb{P}^6$
We describe the geometry of noncommutative deformations of local Calabi-Yau threefolds, showing that the choice of Poisson structure strongly influences the geometry of the quantum moduli space.
Only two ways to construct non-liftable Calabi-Yau threefolds are currently known, one example by Hirokado and one method of Schr\"oer. This article computes some cohomological invariants of these examples of non-liftable Calabi-Yau…
We determine the structure of the BPS algebra of 2-Calabi-Yau Abelian categories for which the stack of objects admits a good moduli space. We prove that this algebra is isomorphic to the positive part of the enveloping algebra of a…
We present a list of arithmetically Gorenstein Calabi-Yau threefolds in $\mathbb{P}^7$ and give evidence that this is a complete list. In particular we construct three new families of arithmetically Gorenstein Calabi-Yau threefolds in…
In this note we search the parameter space of Horrocks-Mumford quintic threefolds and locate a Calabi-Yau threefold which is modular, in the sense that the L-function of its middle-dimensional cohomology is associated to a classical modular…
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 study various examples of Calabi-Yau threefolds over finite fields. In particular, we provide a counterexample to a conjecture of K. Joshi on lifting Calabi-Yau threefolds to characteristic zero. We also compute the p-adic cohomologies…
We study quantum Kahler moduli space of Calabi-Yau fourfolds. Our analysis is based on the recent work by Jockers et al. which gives a novel method to compute the Kahler potential on the quantum Kahler moduli space of Calabi-Yau manifold.…
We study threefolds fibred by K3 surfaces admitting a lattice polarization by a certain class of rank 19 lattices. We begin by showing that any family of such K3 surfaces is completely determined by a map from the base of the family to the…
In this short note we construct Calabi-Yau threefolds with nonabelian fundamental groups of order 64 as quotients of the small resolutions of certain complete intersections of quadrics in $\PP^7$ that were first considered by M. Gross and…
The moduli space of multiply-connected Calabi-Yau threefolds is shown to contain codimension-one loci on which the corresponding variety develops a certain type of hyperquotient singularity. These have local descriptions as discrete…
We study Kustin-Miller unprojections between Calabi-Yau threefolds or more precisely the geometric transitions they induce. We use them to connect many families of Calabi-Yau threefolds with Picard number one to the web of Calabi Yau…
Let $X$ be a normal projective variety admitting a polarized endomorphism $f$, i.e., $f^*H\sim qH$ for some ample divisor $H$ and integer $q>1$. It was conjectured by Broustet and Gongyo that $X$ is of Calabi-Yau type, i.e., $(X,\Delta)$ is…
In this note we construct conifold transitions between several Calabi-Yau threefolds given by Pfaffians in weighted projective spaces and Calabi-Yau threefolds appearing as complete intersections in toric varieties. We use the obtained…
The aim of this paper is to construct families of Calabi--Yau 3-folds without boundary points with maximal unipotent monodromy and to describe the variation of their Hodge structures. In particular five families are constructed. In all…
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…
In this paper, we investigate Keller's deformed Calabi--Yau completion of the derived category of coherent sheaves on a smooth variety. In particular, for an $n$-dimensional smooth variety $Y$, we describe the derived category of the total…
In this paper, we apply Borcea-Voisin's construction and give new examples of fourfolds containing a del Pezzo surface of degree six, which admit an elliptic fibration on a smooth threefold. Some of these fourfolds are Calabi-Yau varieties,…
This note is a report on the observation that some singular varieties admit Calabi--Yau coverings. As an application, we construct 18 new Calabi--Yau 3-folds with Picard number one that have some interesting properties.
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…