Erratum for Boundedness of families of canonically polarized manifolds: A higher dimensional analogue of Shafarevich's conjecture

@article{Kovacs2006ErratumFB,
  title={Erratum for Boundedness of families of canonically polarized manifolds: A higher dimensional analogue of Shafarevich's conjecture},
  author={Sandor J. Kovacs and Max Lieblich},
  journal={Annals of Mathematics},
  year={2006},
  volume={173},
  pages={585-617}
}
We show that the number of deformation types of canonically polarized manifolds over an arbitrary variety with proper singular locus is nite, and that this number is uniformly bounded in any nite type family of base varieties. As a corollary we show that a direct generalization of the geometric version of Shafarevich’s original conjecture holds for innitesimally rigid families of canonically polarized varieties. 
Uniformly effective boundedness of Shafarevich Conjecture-type for families of canonically polarized manifolds
The main result of this note is an effective uniform bound for the number of deformation types of certain nonisotrivial families of canonically polarized manifolds. It extends the author's earlier
Uniformly effective boundedness of Shafarevich Conjecture-type
Abstract The main result of this note is an effective uniform bound for the number of deformation types of certain nonisotrivial families of canonically polarized manifolds. It extends the author's
The Shafarevich conjecture revisited: Finiteness of pointed families of polarized varieties
Motivated by Lang-Vojta's conjectures on hyperbolic varieties, we prove a new version of the Shafarevich conjecture in which we establish the finiteness of pointed families of polarized varieties. We
Néron models and the arithmetic Shafarevich conjecture for certain canonically polarized surfaces
We prove the arithmetic Shafarevich conjecture for canonically polarized surfaces which fibre smoothly over a curve. Our proof uses (1) the theory of Néron models for hyperbolic curves, (2) classical
Brody hyperbolicity of base spaces of certain families of varieties
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
Arakelov inequalities in higher dimensions
. We develop a Hodge theoretic invariant for families of projective mani- folds that measures the potential failure of an Arakelov-type inequality in higher dimensions, one that naturally generalizes
Belyi's theorem for complete intersections of general type
We give a Belyi-type characterisation of smooth complete intersections of general type over $\mathbb{C}$ which can be defined over $\bar{\mathbb{Q}}$. Our proof uses the higher-dimensional analogue
Boundedness in families with applications to arithmetic hyperbolicity
Motivated by conjectures of Demailly, Green-Griffiths, Lang, and Vojta, we show that several notions related to hyperbolicity behave similarly in families. We apply our results to show the
On the Boundedness of Canonical Models
It is conjectured that the canonical models of varieties (not of general type) are bounded when the Iitaka volume is fixed. We confirm this conjecture when the general fibres of the corresponding
On uniformly effective birationality and the Shafarevich Conjecture over curves
Let $B$ be a smooth projective curve of genus $g$, and $S \subset B$ be a finite subset of cardinality $s$. We give an effective upper bound on the number of deformation types of admissible families
...
...

References

SHOWING 1-10 OF 75 REFERENCES
On the Shafarevich conjecture for surfaces of general type over function fields
For a non-isotrivial family of surfaces of general type over a complex projective curve, we give upper bounds for the degree of the direct images of powers of the relative dualizing sheaf. They imply
On Certain Uniformity Properties of Curves Over Function Fields
A uniform version of the Shafarevich Conjecture for function fields (Theorem of Parshin–Arakelov) is proved, together with a uniform version of the geometric Mordell conjecture (Theorem of Manin).
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 scheme M h together with a
Special families of curves, of Abelian varieties, and of certain minimal manifolds over curves
This survey article discusses some results on the structure of families f:V-->U of n-dimensional manifolds over quasi-projective curves U, with semistable reduction over a compactification Y of U. We
Quasi-projective moduli for polarized manifolds
  • E. Viehweg
  • Mathematics
    Ergebnisse der Mathematik und ihrer Grenzgebiete
  • 1995
This text discusses two subjects of quite different natures: construction methods for quotients of quasi-projective schemes either by group actions or by equivalence relations; and properties of
Discreteness of minimal models of Kodaira dimension zero and subvarieties of moduli stacks
We extend some of the results obtained for subvarieties of the moduli stack of canonically polarized manifolds in "Base spaces of non-isotrivial families of smooth minimal models" (math.AG/0103122)
Subvarieties of moduli stacks of canonically polarized varieties : generalizations of Shafarevich ’ s conjecture
DISCLAIMER. In order to understand and follow this article the reader oes notneed to know what a stack is. In fact, the sole point of using the word “ stack” is to make it easier to talk about
Weak Positivity and the Additivity of the Kodaira Dimension for Certain Fibre Spaces
Let V and W be non-singular projective varieties over the field of complex numbers C, n= dim (V) and m=dim (W). Let/: V---+W be a fibre space (this simply means that I is surjective with connected
Compactifications of smooth families and of moduli spaces of polarized manifolds
Let M h be the moduli scheme of canonically polarized manifolds with Hilbert polynomial h. We construct for v ≥ 2 with h(v) > 0 a projective compactification M h of the reduced moduli scheme (M h )
...
...