Related papers: Non-birational Calabi-Yau threefolds that are deri…
A different proof to a known criterion of derived equivalence implying birationality is given. Derived equivalent smooth projective curves over an algebraically closed field are proved to be isomorphic. A different proof of derived…
We show that it is possible to construct supersymmetric three-generation models of Standard Model gauge group in the framework of non-simply-connected elliptically fibered Calabi-Yau, without section but with a bi-section. The fibrations on…
Previously we constructed Calabi-Yau threefolds by a differential-geometric gluing method using Fano threefolds with their smooth anticanonical $K3$ divisors (New York J. Math. 20: 1-33, 2014). In this paper, we further consider the…
We introduce the notion of birational complexity of a log Calabi-Yau pair. This invariant measures how far the log Calabi-Yau pair is to being birational to a toric pair. We study fundamental properties of the new invariant, with a…
First, we classify Calabi-Yau threefolds with infinite fundamental group by means of their minimal splitting coverings introduced by Beauville, and deduce that the nef cone is a rational simplicial cone and any rational nef divisor is…
In the present paper we propose a combinatorial approach to study the so called double octic Clabi--Yau threefolds. We use this description to give a complete classification of double octics with $h^{1,2}\le1$ and to derive their geometric…
(1,d)-polarized abelian surfaces in P^(d-1) with two plane cubic curve fibrations lie in two elliptic P^2-scrolls. The union of these scrolls form a reducible Calabi-Yau 3-fold. In this paper we show that this occurs when d<10 and analyse…
In this paper we construct and classify Lagrangian T^3-fibrations on non compact symplectic manifolds with singular fibres of prescribed topological type. This contributes to the understanding of the structure of the singular fibres that…
We study the limit of Calabi-Yau modular forms, and in particular, those resulting in classical modular forms. We then study two parameter families of elliptically fibred Calabi-Yau fourfolds and describe the modular forms arising from the…
We introduce relative noncommutative Calabi-Yau structures defined on functors of differential graded categories. Examples arise in various contexts such as topology, algebraic geometry, and representation theory. Our main result is a…
We study triples of graded rings defined over the deformation spaces for certain one-parameter families of Calabi-Yau threefolds. These rings are analogues of the rings of modular forms, quasi-modular forms and almost-holomorphic modular…
We prove a structure theorem for the Albanese maps of varieties with Q-linearly trivial log canonical divisors. Our start point is the action of a nonlinear algebraic group on a projective variety.
We investigate a potential relationship between mirror symmetry for Calabi-Yau manifolds and the mirror duality between quasi-Fano varieties and Landau-Ginzburg models. More precisely, we show that if a Calabi-Yau admits a so-called Tyurin…
In this note we provide examples of families of Calabi-Yau 3-manifolds over Shimura varieties, whose mirror families contain subfamilies over Shimura varieties. Therefore these original families and subfamilies on the mirror side contain…
In this paper, the relationship between the existence of special lagrangian submanifolds and the collapsing of Calabi-Yau manifolds is studied. First, special lagrangian fibrations are constructed on some regions of bounded curvature and…
Let $X$ be a smooth projective $n$-fold such that $q(X)=0$ and $L$ a globally generated, big line bundle on $X$ such that $h^0(K_X+(n-2)L) >0$. We give necessary and sufficient conditions for the adjoint systems $|K_X+kL|$ to be birational…
We discuss the possibility of the extension of the duality between the webs of heterotic string and the type IIA string to Calabi-Yau 3-folds with another K3 fiber by comparing the dual polyhedron of Calabi-Yau 3-folds given by Candelas,…
In this paper we deal with Calabi-Yau structures associated with (differential graded versions of) deformed multiplicative preprojective algebras, of which we provide concrete algebraic descriptions. Along the way, we prove a general result…
We describe two ways to construct finite rational morphisms between fiber products of rational elliptic surfaces with section and some Calabi--Yau manifolds. We use them to construct correspondences between such fiber products that admit at…
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…