21 Result(s)

Article

Picard theorems for moduli spaces of polarized varieties

As a result of our study of the hyperbolicity of the moduli space of polarized manifold, we give a general big Picard theorem for a holomorphic curve on a log-smooth pair (X, D) such that

Ya Deng, Steven Lu, Ruiran Sun, Kang Zuo in Mathematische Annalen (2023)

Article

The Oort Conjecture for Shimura Curves of Small Unitary Rank

We prove that a Shimura curve in the Siegel modular variety is not generically contained in the open Torelli locus as long as the rank of unitary part in its canonical Higgs bundle satisfies a numerical upper ...

Ke Chen, **n Lu, Kang Zuo in Communications in Mathematics and Statistics (2018)

Article

Singular fibers and Kodaira dimensions

Let \(f:\,X \rightarrow \mathbb {P}^1\) f ...

**n Lu, Sheng-Li Tan, Kang Zuo in Mathematische Annalen (2018)

Article

Canonical class inequality for fibred spaces

We establish the canonical class inequality for families of higher dimensional projective manifolds. As an application, we get a new inequality between the Chern numbers of threefolds X with smooth families of mi...

Jun Lu, Sheng-Li Tan, Kang Zuo in Mathematische Annalen (2017)

Article

A new inequality on the Hodge number \(h^{1,1}\) of algebraic surfaces

We get a new inequality on the Hodge number \(h^{1,1}(S)\) ...

Jun Lu, Sheng-Li Tan, Fei Yu, Kang Zuo in Mathematische Zeitschrift (2014)

Article

On the monodromy of the moduli space of Calabi–Yau threefolds coming from eight planes in \({\mathbb{P}^3}\)

It is a fundamental problem in geometry to decide which moduli spaces of polarized algebraic varieties are embedded by their period maps as Zariski open subsets of locally Hermitian symmetric domains. In the p...

Ralf Gerkmann, Mao Sheng, Duco van Straten, Kang Zuo in Mathematische Annalen (2013)

Article

Polarized variation of Hodge structures of Calabi–Yau type and characteristic subvarieties over bounded symmetric domains

In this paper, we extend the construction of the canonical polarized variation of Hodge structures over tube domain considered by Gross (Math Res Lett 1:1–9, 1994) to bounded symmetric domain and introduce a s...

Mao Sheng, Kang Zuo in Mathematische Annalen (2010)

Article

Calabi–Yau varieties with semi-stable fibre structures

Motivated by the Strominger–Yau–Zaslow conjecture, we study Calabi–Yau varieties with semi-stable fibre structures. We use Hodge theory to study the higher direct images of wedge products of relative cotangent...

Yi Zhang, Kang Zuo in manuscripta mathematica (2008)

Chapter

Special Families of Curves, of Abelian Varieties, and of Certain Minimal Manifolds over Curves

Martin Möller, Eckart Viehweg, Kang Zuo in Global Aspects of Complex Geometry (2006)

Chapter

Base Spaces of Non-Isotrivial Families of Smooth Minimal Models

Given a polynomial h of degree n let M _h be the moduli functor of canonically polarized complex manifolds with Hilbert polynomial _h. By [23] there exist a quasi-projective ...

Eckart Viehweg, Kang Zuo in Complex Geometry (2002)

Chapter

Preliminaries

Kang Zuo in Representations of Fundamental Groups of Algebraic Varieties (1999)

Chapter

Introduction

Kang Zuo in Representations of Fundamental Groups of Algebraic Varieties (1999)

Chapter

Harmonic metrics on flat vector bundles

Kang Zuo in Representations of Fundamental Groups of Algebraic Varieties (1999)

Chapter

Shafarevich maps for representations of fundamental groups, Kodaira dimension and Chernhyperbolicity of Shafarevich varieties

Kang Zuo in Representations of Fundamental Groups of Algebraic Varieties (1999)

Chapter

Non-abelian Hodge theory, factorization theorems for non rigid or p-adic unbounded representations

Kang Zuo in Representations of Fundamental Groups of Algebraic Varieties (1999)

Article

Factorizations of nonrigid Zariski dense representations of π₁ of projective algebraic manifolds

Kang Zuo in Inventiones mathematicae (1994)

Article

Some structure theorems for semi-simple representations of π₁ of algebraic manifolds

Kang Zuo in Mathematische Annalen (1993)