# Families of varieties of general type over compact bases

@article{Kebekus2007FamiliesOV,
title={Families of varieties of general type over compact bases},
author={Stefan Kebekus and Sandor J. Kovacs},
year={2007},
volume={218},
pages={649-652}
}
• Published 19 April 2007
• Mathematics
• Mathematics
Journal 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
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
• Mathematics
manuscripta 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
• Mathematics
Algebra & 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
• 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
• 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]
• 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
• 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
• Mathematics
Inventiones 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
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

• 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
• 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
• 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
• 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
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 $p$
• 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
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