arXiv research

Let $X$ be a complex four-dimensional compact Calabi-Yau manifold equipped with a Kähler form $ω$ and a holomorphic four-form $Ω$. Under certain assumptions, we define Donaldson-Thomas type deformation invariants by studying the moduli space of the solutions of Donaldson-Thomas equations on the given Calabi-Yau manifol…

Machine learning predicts Hodge numbers of Calabi-Yau four-folds.

In this paper we study several issues related to the generation of superpotential induced by background Ramond-Ramond fluxes in compactification of Type IIA string theory on Calabi-Yau four-folds. Identifying BPS solitons with D-branes wrapped over calibrated submanifolds in a Calabi-Yau space, we propose a general for…

New potentials found for sheaves on Calabi-Yau 4-folds.

Study complex deformations of compact complex surfaces in Calabi-Yau four-folds.

Study on deformations of singular submanifolds in complex geometry.

New Spin(7)-manifolds constructed via generalized connected sums.

Machine learning approximates Calabi-Yau Hodge numbers from weight systems.

Let $({\bf X},ω_{\bf X}^*)$ be a separated, $-2$-shifted symplectic derived $\mathbb C$-scheme, in the sense of Pantev, Toen, Vezzosi and Vaquie arXiv:1111.3209, of complex virtual dimension ${\rm vdim}_{\mathbb C}{\bf X}=n\in\mathbb Z$, and $X_{\rm an}$ the underlying complex analytic topological space. We prove that …

Let K be a connected finite complex. This paper studies the problem of whether one can attach a cell to some iterated suspension S^j K so that the resulting space satisfies Poincare duality. When this is possible, we say that S^j K is a spine. We introduce the notion of quadratic self duality and show that if K is quad…

The Hodge Conjecture is equivalent to a statement about conditions under which a complex vector bundle on a smooth complex projective variety admits a holomorphic structure. I advertise a class of abelian four-folds due to Mumford where this approach could be tested. I construct explicit smooth vector bundles - which c…

We construct periodic families of Poincare complexes, partially solving a question of Hodgson that was posed in the proceedings of the 1982 Northwestern homotopy theory conference. We also construct infinite families of Poincare complexes whose top cell falls off after one suspension but which fail to embed in a sphere…

In the first part we survey some of the known results and conjectures on compact Hyperkaehler (HK) manifolds. In the second part we presents a program which aims to show that HK four-folds whose second cohomology (with 4-tuple cup-product) is isomorphic to that of the Hilbert square of a K3 enjoy many of the beautiful …

Constructs complete Calabi-Yau metrics from smoothed Calabi-Yau intersections.

New examples of Calabi-Yau 3-folds with unique properties.

Uniform estimates for Calabi-Yau degenerations proved.

Study classifies Calabi-Yau threefolds with non-Gorenstein involutions.

Researchers use gluing method to describe collapsing Calabi-Yau metrics on K3 fibred 3-folds.

Polyhomogeneous expansions for Calabi-Yau metrics near singularities.

New Calabi-Yau metrics constructed with detailed geometry at infinity.

We study Calabi-Yau 3-folds M_0 with a conical singularity x modelled on a Calabi-Yau cone V. We construct desingularizations of M_0, obtaining a 1-parameter family of compact, nonsingular Calabi-Yau 3-folds which has M_0 as the limit. The way we do is to choose an Asymptotically Conical Calabi-Yau 3-fold Y modelled on…

In this paper, we study the analogue of the Shafarevich conjecture for polarized Calabi-Yau varieties. We use variations of Hodge structures and Higgs bundles to establish a criterion for the {\it rigidity} of families. We then apply the criterion to obtain that some important and typical families of Calabi-Yau varieti…

Solves Calabi-Yau equation on complex manifolds with non-positive astheno-Ricci curvature.

In this paper, we construct simply connected symplectic Calabi-Yau 6-manifolds by applying Gompf's symplectic fiber sum operation along $T^4$. Using our construction, we also produce symplectic non-Kähler Calabi-Yau 6-manifolds with fundamental group $\Z$. In this paper, we also produce the first examples of simply con…

New Calabi-Yau metrics converge polynomially to Calabi model space.

Holomorphic connections on Calabi-Yau manifolds are flat.

Sharp diameter bounds for Calabi-Yau degenerations proved.

Survey on decorated marked surfaces for Calabi-Yau categories.

Gluing theorem for collapsing warped-QAC Calabi-Yau manifolds verified.

Constructs BCOV invariant for Calabi-Yau pairs.

This note is a report on the observation that some singular varieties admit Calabi--Yau coverings. As an application, we construct 18 new Calabi--Yau 3-folds with Picard number one that have some interesting properties.

The study examines equivalences in Calabi-Yau manifolds' metrics and classes.

Study on Calabi-Yau metrics and their degenerations.

Constructs special Lagrangian submanifolds in Calabi-Yau 3-folds.

Study noncommutative deformations of Calabi-Yau threefolds.

A generalized Calabi-Yau structure is a geometrical structure on a manifold which generalizes both the concept of the Calabi-Yau structure and that of the symplectic one. In view of a result of Lin and Tolman in generalized complex cases, we introduce in this paper the notion of a generalized moment map for a compact L…

Study on collapsing Calabi-Yau manifolds and their metrics.

The paper describes Calabi-Yau structures and special Lagrangian submanifolds in complexified symmetric spaces.

Complete Calabi-Yau metrics made on special 3D spaces.

Study shows Calabi-Yau metrics converge to a specific form under certain conditions.

Complete Calabi-Yau metrics on abelian fibrations over complex space.

Proves certain Calabi-Yau varieties are projective.

Constructs non-Kähler Calabi-Yau 3-folds with large Betti numbers.

Study the limit of Calabi-Yau metrics with degenerate skeletons.

Constructs Calabi-Yau metrics on 3-folds with properties similar to Taub-NUT and Ooguri-Vafa.

Study on Calabi-Yau locally conformally Kähler manifolds proving they are Vaisman.

Global estimates improved for collapsing Calabi-Yau metrics on K3 surfaces.

New proof of Weil-Petersson metric for Calabi-Yau varieties.