相关论文: Calabi-Yau metrics with cone singularities along i…

We prove a new rigidity criterion for families of polarized Calabi-Yau manifolds. Motivated by known non-rigid examples, we conjecture that a family over a quasi-projective curve is rigid if it admits a smooth compactification whose…

We consider a generalization of Einstein-Sasaki manifolds, which we characterize in terms both of spinors and differential forms, that in the real analytic case corresponds to contact manifolds whose symplectic cone is Calabi-Yau. We…

It is shown that any affine toric variety Y, which is Q-Gorenstein, admits a conical Ricci flat Kahler metric, which is smooth on the regular locus of Y. The corresponding Reeb vector is the unique minimizer of the volume functional on the…

We establish a new weak coupling limit in F-theory. The new limit may be thought of as the process in which a local model bubbles off from the rest of the Calabi-Yau. The construction comes with a small deformation parameter $t$ such that…

By using the global deformation of almost complex structures which are compatible with a symplectic form off a Lebesgue measure zero subset, we construct a (measurable) Lipschitz Kahler metric such that the one-form type Calabi-Yau equation…

We construct new complete Calabi-Yau metrics on the complement of an anticanonical divisors $D$ in a Fano manifold of dimension at least three, when $D$ consists of two transversely intersecting smooth divisors. The asymptotic geometry is…

We show boundedness of polarized Calabi--Yau fibrations over curves only with fixed volumes of general fibers and Iitaka volumes. As its application, we construct a separated coarse moduli space of K-stable Calabi-Yau fibrations over curves…

We study Kustin--Miller unprojections of Calabi--Yau threefolds. As an application we work out the geometric properties of Calabi--Yau threefolds defined as linear sections of determinantal varieties. We compute their Hodge numbers and…

We prove existence of Yamabe metrics on singular manifolds with conical points and conical links of Einstein type that include orbifold structures. We deal with metrics of generic type and derive a counterpart of Aubin's classical result.…

Multiply-connected Calabi-Yau threefolds are of particular interest for both string theorists and mathematicians. Recently it was pointed out that one of the generic degenerations of these spaces (occurring at codimension one in moduli…

Recent progress in the deformation theory of Calabi-Yau varieties $Y$ with canonical singularities has highlighted the key role played by the higher Du Bois and higher rational singularities, and especially by the so-called $k$-liminal…

We use a generalization of the Gibbons-Hawking ansatz to study the behavior of certain non-compact Calabi-Yau manifolds in the large complex structure limit. This analysis provides an intermediate step toward proving the metric collapse…

In this paper we investigate the $\mathbb{Q}$-rational points of a class of simply connected Calabi-Yau threefolds, which were originally studied by Hosono and Takagi in the context of mirror symmetry. These varieties are defined as a…

Given a polarized family of varieties over the unit disc, smooth except over the origin and with smooth fibers Calabi-Yau, we show that the origin lies at finite Weil-Petersson distance if and only if after a finite base change the family…

Recently Knutsen found criteria for the curves in a complete linear system $|\mathcal{L}|$ on a smooth surface $X$ in a nodal K-trivial threefold $Y_0$ to deform to a scheme of finitely many smooth isolated curves in a general deformation…

Finding Ricci-flat (Calabi-Yau) metrics is a long standing problem in geometry with deep implications for string theory and phenomenology. A new attack on this problem uses neural networks to engineer approximations to the Calabi-Yau metric…

In this article we study the deformation theory of conically singular Cayley submanifolds. In particular, we prove a result on the expected dimension of a moduli space of Cayley deformations of a conically singular Cayley submanifold.…

We show that any asymptotically Calabi manifold which is Calabi-Yau can be compactified complex analytically to a weak Fano manifold. Furthermore, the Calabi-Yau structure arises from a generalized Tian-Yau construction on the…

Let $X$ be a complex projective variety with only canonical singularities and with trivial canonical bundle. Let $L$ be an ample line bundle on $X$. Assume that the pair $(X,L)$ is the flat limit of a family of smooth polarized Calabi-Yau…

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…