Related papers: Non-birational Calabi-Yau threefolds that are deri…

Given X a K3 surface, a mirror dual to X can be identified with a component of the moduli space of semistable sheaves on X. We consider fibrations by K3 surfaces over a one dimensional base that are Calabi-Yau and we obtain a dual fibration…

We prove that up to birational equivalence, there exists only a finite number of families of Calabi-Yau threefolds (i.e. a threefold with trivial canonical class and factorial terminal singularities) which have an elliptic fibration to a…

We provide a fine classification of Gorenstein quotients of three-dimensional abelian varieties with isolated singularities, up to biholomorphism and homeomorphism. This refines a result of Oguiso and Sakurai about fibred Calabi-Yau…

Let X and Y be two smooth projective n-dimensional algebraic varieties X and Y over C with trivial canonical line bundles. We use methods of p-adic analysis on algebraic varieties over local number fields to prove that if X and Y are…

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…

We present two proofs for a bound on the rank of the Mordell-Weil group of some elliptic fibrations. The bounds apply to Calabi-Yau varieties, which are also of interest to the physics of string theory. We prove explicit bounds for…

The concept of non-Gorenstein involutions on Calabi-Yau threefolds is a higher dimensional generalization of non-symplectic involutions on $K3$ surfaces. We present some elementary facts about Calabi-Yau threefolds with non-Gorenstein…

For each pair of elliptic Calabi--Yau $3$-folds in the list of Knapp--Scieidegger--Schimannek \cite{2107.05647}, we prove that they are derived-equivalent linear over the base. Except one self-dual pair, each yields two families of smooth…

We discuss the question of finding conditions on a derived equivalence between two smooth projective varieties $X$ and $Y$ that imply that $X$ and $Y$ are birational. The types of conditions we consider are in the spirit of finding…

We formulate some precise conjectures concerning the existence and structure of supersymmetric T3 fibrations of Calabi-Yau threefolds, and describe how these conjectural fibrations would give rise to the Strominger-Yau-Zaslow version of…

We systematically analyze the fibration structure of toric hypersurface Calabi-Yau threefolds with large and small Hodge numbers. We show that there are only four such Calabi-Yau threefolds with $h^{1, 1} \geq 140$ or $h^{2, 1} \geq 140$…

In part I of this paper we constructed certain fibered Calabi-Yaus by a quotient construction in the context of weighted hypersurfaces. In this paper look at the case of K3 fibrations more closely and study the singular fibers which occur.…

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…

In this paper we prove the existence and uniqueness of the form-type Calabi-Yau equation on K\"ahler manifolds of nonnegative orthogonal bisectional curvature.

Ito-Miura-Okawa-Ueda have constructed a pair of Calabi-Yau threefolds $X$ and $Y$ that are L-equivalent and derived equivalent, but not stably birational. We complete the picture by showing that $X$ and $Y$ have isomorphic Chow motives.

We study Calabi--Yau 3-folds with infinitely many divisorial contractions. We also suggest a method to describe Calabi--Yau 3-folds with the infinite automorphism group.

We construct a general class of Calabi--Yau threefolds from fiber products of rational elliptic surfaces with section, generalizing a construction of Schoen to include all Kodaira fiber types. The resulting threefolds each have two elliptic…

In the studies on the modularity conjecture for rigid Calabi-Yau threefolds several examples with the unique level 8 cusp form were constructed. According to the Tate Conjecture correspondences inducing isomorphisms on the middle…

We investigate fibrations by non-hyperelliptic curves of arithmetic genus three and geometric genus one in characteristic two. Assuming that there is only one moving singularity and that its image in the Frobenius pullback of the fibration…

Given a pair of derived-equivalent Calabi--Yau manifolds of dimension more than two, we prove that the derived equivalence can be extended to general fibers of versal deformations. As an application, we give a new proof of the…