Related papers: Calabi-Yau Threefolds Fibred by Mirror Quartic K3 …
The limiting procedure of special Kahler manifolds to their rigid limit is studied for moduli spaces of Calabi-Yau manifolds in the neighbourhood of certain singularities. In two examples we consider all the periods in and around the rigid…
We introduce some new algebraic structures arising naturally in the geometry of Calabi-Yau manifolds and mirror symmetry. We give a universal construction of Calabi-Yau algebras in terms of a noncommutative symplectic DG algebra resolution.…
Mumford constructed a family of abelian fourfolds with special stucture not characterized by endomorphism ring. Galluzzi showed that the weight 2 Hodge structure of such a variety decomposes into Hodge substructures via the action of…
We construct smooth Calabi-Yau threefolds Z, torus-fibered over a dP_9 base, with fundamental group Z_2 X Z_2. To do this, the structure of rational elliptic surfaces is studied and it is shown that a restricted subset of such surfaces…
In this note we speculate about the structure of maximal product subvarieties in moduli stacks of Calabi-Yau manifolds. We discuss examples for quintic hypersurfaces in the four dimensional projective space.
We define the notion of mirror of a Calabi-Yau manifold with a stable bundle in the context of type II strings in terms of supersymmetric cycles on the mirror. This allows us to relate the variation of Hodge structure for cohomologies…
In this work, we study the local zeta functions of Calabi-Yau fourfolds. This is done by developing arithmetic deformation techniques to compute the factor of the zeta function that is attributed to the horizontal four-form cohomology.…
We investigate mirror symmetry for toric Calabi-Yau manifolds from the perspective of the SYZ conjecture. Starting with a non-toric special Lagrangian torus fibration on a toric Calabi-Yau manifold $X$, we construct a complex manifold…
This is a survey of the geometry of complex cubic fourfolds with a view toward rationality questions. Topics include classical constructions of rational examples, Hodge structures and special cubic fourfolds, associated K3 surfaces and…
A K3 surface is a quaternionic analogue of an elliptic curve from a view point of moduli of vector bundles. We can prove the algebraicity of certain Hodge cycles and a rigidity of curve of genus eleven and gives two kind of descriptions of…
We give a complete classification of finite subgroups of automorphisms of K3 surfaces up to deformation. The classification is in terms of Hodge theoretic data associated to certain conjugacy classes of finite subgroups of the orthogonal…
This is a survey of the Kawamata-Morrison cone conjecture on the structure of Calabi-Yau varieties and more generally Calabi-Yau pairs. We discuss the proof of the cone conjecture for algebraic surfaces, with plenty of examples. We show…
We consider smooth complete intersection Calabi-Yau 3-folds in minuscule Schubert varieties, and study their mirror symmetry by degenerating the ambient Schubert varieties to Hibi toric varieties. We list all possible Calabi-Yau 3-folds of…
This paper continues the study initiated in [ISZ25] on the moduli of surfaces admitting lc-trivial fibrations. Using the techniques developed in [ISZ25], we (1) provide a classification of the surfaces appearing on the boundary of the…
The 2-dimensional Lyness map is a 5-periodic birational map of the plane which may famously be resolved to give an automorphism of a log Calabi-Yau surface, given by the complement of an anticanonical pentagon of $(-1)$-curves in a del…
We obtain a detailed classification for a class of non-simply connected Calabi-Yau threefolds which are of potential interest for a wide range of problems in string phenomenology. These threefolds arise as quotients of Schoen's Calabi-Yau…
SYZ mirror conjecture predicts that a Calabi-Yau manifold $X$ consists of a family of tori which are dual to a family of special lagrangian tori on the mirror dual manifold $\hat{X}$. Here we consider a fibration of polarized abelian…
Motivated by the picture of mirror symmetry suggested by Strominger, Yau and Zaslow, we made a conjecture concerning the Gromov-Hausdorff limits of Calabi-Yau n-folds (with Ricci-flat K\"ahler metric) as one approaches a large complex…
In this paper, the numbers of rational curves on general complete intersection Calabi-Yau threefolds in complex projective spaces are computed up to degree six. The results are all in agreement with the predictions made from mirror…
In this paper, we make progress on understanding the collapsing behavior of Calabi-Yau metrics on a degenerating family of polarized Calabi-Yau manifolds. In the case of a family of smooth Calabi-Yau hypersurfaces in projective space…