## 37 Citations

### On the hyperbolicity of base spaces for maximally variational families of smooth projective varieties

- MathematicsJournal of the European Mathematical Society
- 2021

For smooth families with maximal variation, whose general fibers have semi-ample canonical bundle, the generalized Viehweg hyperbolicity conjecture states that the base spaces of such families are of…

### Families of canonically polarized manifolds over log Fano varieties

- MathematicsCompositio Mathematica
- 2013

Abstract Let $(X,D)$ be a dlt pair, where $X$ is a normal projective variety. We show that any smooth family of canonically polarized varieties over $X\setminus \,{\rm Supp}\lfloor D \rfloor $ is…

### Isotriviality of smooth families of varieties of general type

- Mathematicsmanuscripta mathematica
- 2022

In this paper, we proved that a log smooth family of log general type klt pairs with a special (in the sense of Campana) quasi-projective base is isotrivial. As a consequence, we proved the…

### Brody hyperbolicity of base spaces of certain families of varieties

- MathematicsAlgebra & Number Theory
- 2019

We prove that quasi-projective base spaces of smooth families of minimal varieties of general type with maximal variation do not admit Zariski dense entire curves. We deduce the fact that moduli…

### Hodge sheaves underlying flat projective families

- Mathematics
- 2021

We show that for any fixed weight there is a natural system of Hodge sheaves whose Higgs field has no poles arising from a flat projective family of varieties parametrized by a regular complex base…

### Fano varieties 14 L 30 Group actions on varieties or schemes ( quotients ) 14 E 20 Coverings in algebraic geometry Keywords : finite group actions on log Fano pairs ; equivariant K-stability ; K-moduli of Fano varieties

- Mathematics
- 2022

References: [1] Alper, J., Blum, H., Halpern-Leistner, D. and Xu, C., Reducitivity of the automorphism group of K-polystable Fano varieties,Invent. Math.222(3) (2020) 995-1032. · Zbl 1465.14043 [2]…

### Kebekus lectures on differential forms on singular spaces by Mateusz Micha lek

- Mathematics
- 2011

1.1 Classical theory Let us first recall basic facts that are the motivation for further constructions. Fact 1.1. Let X be a smooth, projective variety of dimension n over C. There exist the sheaf of…

### Viehweg’s hyperbolicity conjecture for families with maximal variation

- Mathematics
- 2015

We use the theory of Hodge modules to construct Viehweg–Zuo sheaves on base spaces of families with maximal variation and fibers of general type and, more generally, families whose geometric generic…

### Viehweg’s hyperbolicity conjecture for families with maximal variation

- MathematicsInventiones mathematicae
- 2016

We use the theory of Hodge modules to construct Viehweg–Zuo sheaves on base spaces of families with maximal variation and fibers of general type and, more generally, families whose geometric generic…

### On properness of K-moduli spaces and optimal degenerations of Fano varieties

- Mathematics
- 2020

We establish an algebraic approach to prove the properness of moduli spaces of K-polystable Fano varieties and reduce the problem to a conjecture on destabilizations of K-unstable Fano varieties.…

## References

SHOWING 1-10 OF 11 REFERENCES

### Families of canonically polarized varieties over surfaces

- Mathematics
- 2005

Shafarevich’s hyperbolicity conjecture asserts that a family of curves over a quasi-projective 1-dimensional base is isotrivial unless the logarithmic Kodaira dimension of the base is positive. More…

### The structure of surfaces mapping to the moduli stack of canonically polarized varieties

- Mathematics
- 2007

Generalizing the well-known Shafarevich hyperbolicity conjecture, it has been conjectured by Viehweg that a quasi-projective manifold that admits a generically finite morphism to the moduli stack of…

### Existence of Rational Curves on Algebraic Varieties, Minimal Rational Tangents, and Applications

- Mathematics
- 2006

This survey paper discusses some of the recent progress in the study of rational curves on algebraic varieties. It was written for the survey volume of the priority programme "Global Methods in…

### Base Spaces of Non-Isotrivial Families of Smooth Minimal Models

- Mathematics
- 2002

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 scheme M h together with a…

### Global aspects of complex geometry

- Mathematics
- 2006

Ingrid C. Bauer and Fabrizio Catanese and Roberto Pignatelli: Complex surfaces of general type: some recent progress Manuel Blickle, HA(c)lAne Esnault, Kay RA lling: Characteristic 0 and $p$…

### Rationally connected foliations after Bogomolov and McQuillan

- Mathematics
- 2005

This paper is concerned with a sufficient criterion to guarantee that a given foliation on a normal variety has algebraic and rationally connected leaves. Following ideas from a preprint of…

### Deformations of a morphism along a foliation and applications

- Geology
- 1987

A prefabricated log building has walls formed by horizontally extending, vertically stacked log courses joined by tongue and groove joints. The walls are joined at corners by mortise and tenon…

### ALGEBRAIC GEOMETRY An Introduction to Birational Geometry of Algebraic Varieties (Graduate Texts in Mathematics, 76)

- Mathematics
- 1983