Related papers: A global Torelli theorem for certain Calabi-Yau th…

We prove a generic Torelli theorem for a class of three-dimensional log Calabi--Yau pairs $(Y, D)$ with maximal boundary.

In this paper, a family of smooth multiply connected Calabi--Yau threefolds is investigated. The family presents a counterexample to global Torelli as conjectured by Aspinwall and Morrison.

The result of this paper is proved in arXiv:1112.1163

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…

We develop the deformation theory of Calabi-Yau threefolds, by which we mean 3-dimensional complex manifolds with a nowhere-vanishing holomorphic 3-form, on manifolds with boundary. The boundary data is a closed, real 3-form on the…

We describe the proof that the period map from the Torelli space of Calabi-Yau manifolds to the classifying space of polarized Hodge structures is an embedding. The proof is based on the constructions of holomorphic affine structure on the…

To a one-parameter family of Calabi-Yau threefolds, we can associate the extended period map by the log Hodge theory of Kato and Usui. In the present paper, we study the image of a maximally unipotent monodromy point under the extended…

A well-known theorem of Kulikov, Persson and Pinkham states that a degeneration of a family of K3-surfaces with trivial monodromy can be completed to a smooth family. We give a simple example that an analogous statement does not hold for…

We present a method for computing the generic degree of a period map defined on a quasi-projective surface. As an application, we explicitly compute the generic degree of three period maps underlying families of Calabi-Yau 3-folds coming…

This paper first generalises the Bogomolov-Tian-Todorov unobstructedness theorem to the case of Calabi-Yau threefolds with canonical singularities. The deformation space of such a Calabi-Yau threefold is no longer smooth, but the general…

We give an effective infinitesimal Torelli theorem for cyclic covers of G/P, where G is a simple algebraic group and P is a maximal parabolic subgroup.

We formulate the modularity conjecture for rigid Calabi-Yau threefolds defined over the field Q of rational numbers. We establish the modularity for the rigid Calabi-Yau threefold arising from the root lattice A_3. Our proof is based on…

We prove a sort of reconstruction theorem for generic elliptic Calabi-Yau $3$-folds in the sense of C\u{a}ld\u{a}raru. From our argument it follows that two generic elliptic Calabi-Yau $3$-folds are derived-equivalent linear over the base…

Any Calabi-Yau threefold X with infinite fundamental group admits an \'etale Galois covering either by an abelian threefold or by the product of a K3 surface and an elliptic curve. We call X of type A in the former case and of type K in the…

We give a criterion for a continuous family of curves on a nodal $K$-trivial threefold $X_0$ to contribute geometrically rigid curves to a general smoothing of $X_0$. As an application, we prove the existence of geometrically rigid curves…

The proof of Serre's conjecture on Galois representations over finite fields allows us to show, using a method due to Serre himself, that all rigid Calabi-Yau threefolds defined over Q are modular.

We propose a generalization of Verbitsky's global Torelli theorem in the framework of compact K\"ahler irreducible holomorphically symplectic orbifolds by adapting Huybrechts' proof (arXiv:1106.5573). As intermediate step needed, we also…

We prove a categorical version of the Torelli theorem for cubic threefolds. More precisely, we show that the non-trivial part of a semi-orthogonal decomposition of the derived category of a cubic threefold characterizes its isomorphism…

In this note, we give a short proof of the Torelli theorem for cubic fourfolds that relies on the global Torelli theorem for irreducible holomorphic symplectic varieties proved by Verbitsky.

In this paper, we prove the rational coefficient case of the global ACC for foliated threefolds. Specifically, we consider any lc foliated log Calabi-Yau triple $(X,\mathcal{F},B)$ of dimension $3$ whose coefficients belong to a set…