Related papers: Valuative independence for Calabi--Yau varieties
We study moduli stabilization of the F-theory compactified on an elliptically fibered Calabi-Yau fourfold. Our setup is based on the mirror symmetry framework including brane deformations. The complex structure moduli dependence of the…
An explicit description of the spectral data of stable U(n) vector bundles on elliptically fibered Calabi-Yau threefolds is given, extending previous work of Friedman, Morgan and Witten. The characteristic classes are computed and it is…
We construct BCOV invariant for Calabi-Yau pairs. The construction covers the classical BCOV invariant and certain equivariant BCOV invariant. The BCOV invariant obtained is expected to be well-behaved under birational equivalence.
Long ago, Nemeschansky and Sen demonstrated that the Ricci-flat metric on a Calabi-Yau manifold could be corrected, order by order in perturbation theory, to produce a conformally invariant (2,2) nonlinear sigma model. Here we extend this…
We study the birational boundedness of special fibers of log Calabi-Yau fibrations and Fano fibrations. We show that for a locally stable family of Fano varieties or polarised log Calabi-Yau pairs over a curve, if the general fiber…
In this thesis we study the relationship between the existence of canonical metrics on a complex manifold and stability in the sense of geometric invariant theory. We introduce a modification of K-stability of a polarised variety which we…
Recent results on duality between string theories and connectedness of their moduli spaces seem to go a long way toward establishing the uniqueness of an underlying theory. For the large class of Calabi-Yau 3-folds that can be embedded as…
For polarised degenerations of Calabi-Yau manifolds whose essential skeleton has dimension $1\leq m\leq n$, we show that the $C^0$ potential theoretic limit of the Calabi-Yau metrics agrees with the non-archimedean Calabi-Yau metric on the…
We use the gradients of theta functions at odd two-torsion points --- thought of as vector-valued modular forms --- to construct holomorphic differential forms on the moduli space of principally polarized abelian varieties, and to…
Theta functions were defined for varieties with effective anticanonical divisor and are related to certain punctured Gromov-Witten invariants. In this paper we show that in the case of a log Calabi-Yau surface (X,D) with smooth very ample…
After providing an explicit K-stability condition for a $\mathbb{Q}$-Gorenstein log spherical cone, we prove the existence and uniqueness of an equivariant K-stable degeneration of the cone, and deduce uniqueness of the asymptotic cone of a…
We construct many new non-liftable three-dimensional Calabi-Yau spaces in positive characteristic. The technique relies on lifting a nodal model to a smooth rigid Calabi-Yau space over some number field as introduced by the first author and…
In this technical note we describe a new (to the physics literature) construction of bundles on Calabi-Yaus. We primarily study this construction in the special case of K3 surfaces, for which interesting results can be obtained. For…
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 $q>1$. Then Broustet and Gongyo proposed the conjecture that $X$ is of Calabi-Yau type (CY for short),…
We apply results on inducing stability conditions to local Calabi-Yau threefolds and obtain applications to Donaldson-Thomas (DT) theory. A basic example is the total space of the canonical bundle of $Z=\mathbb{P}^1\times \mathbb{P}^1$. We…
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 give a method to construct Calabi-Yau metrics on G-invariant vector bundles over Kahler coset spaces G/H using supersymmetric nonlinear realizations with matter coupling. As a concrete example we discuss the CP^N model coupled with…
We study heterotic Calabi--Yau compactifications with NSNS three-form flux in view of moduli stabilisation and investigate whether the value $|W_0|$ of the flux superpotential evaluated at supersymmetric minima can be small. Unlike in type…
We construct several examples of higher-dimensional Calabi-Yau manifolds and prove their modularity.
We construct, as hypersurfaces in toric varieties, Calabi-Yau manifolds corresponding to F-theory vacua dual to E8*E8 heterotic strings compactified to six dimensions on K3 surfaces with non-semisimple gauge backgrounds. These vacua were…