The construction problem for Hodge numbers modulo an integer

@article{Paulsen2019TheCP,
  title={The construction problem for Hodge numbers modulo an integer},
  author={Matthias Paulsen and S. Schreieder},
  journal={Algebra \& Number Theory},
  year={2019},
  volume={13},
  pages={2427-2434}
}
For any integer m ≥ 2 and any dimension n ≥ 1, we show that any ndimensional Hodge diamond with values in Z/mZ is attained by the Hodge numbers of an n-dimensional smooth complex projective variety. As a corollary, there are no polynomial relations among the Hodge numbers of n-dimensional smooth complex projective varieties besides the ones induced by the Hodge symmetries, which answers a question raised by Kollár in 2012. 
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References

SHOWING 1-10 OF 22 REFERENCES
The construction problem for Hodge numbers modulo an integer in positive characteristic
Abstract Let k be an algebraically closed field of positive characteristic. For any integer $m\ge 2$ , we show that the Hodge numbers of a smooth projective k-variety can take on any combination ofExpand
On the construction problem for Hodge numbers
For any symmetric collection of natural numbers h^{p,q} with p+q=k, we construct a smooth complex projective variety whose weight k Hodge structure has these Hodge numbers; if k=2m is even, then weExpand
Geometric Hodge structures with prescribed Hodge numbers
Call a pure Hodge structure geometric if it is contained in the cohomology of a smooth complex projective variety. The main goal is to show that for any set of Hodge numbers (subject to the obviousExpand
The Hodge ring of Kähler manifolds
Abstract We determine the structure of the Hodge ring, a natural object encoding the Hodge numbers of all compact Kähler manifolds. As a consequence of this structure, there are no unexpectedExpand
Higher direct images of the structure sheaf in positive characteristic
We prove vanishing of the higher direct images of the structure (and the canonical) sheaf for a proper birational morphism with source a smooth variety and target the quotient of a smooth variety byExpand
The Construction Problem in Kähler Geometry
One of the most surprising things in algebraic geometry is the fact that algebraic varieties over the complex numbers benefit from a collection of metric properties which strongly influence theirExpand
Resolution of singularities for 3-folds in positive characteristic
A concise, complete proof of resolution of singularities of 3-folds in positive characteristic $>5$ is given. Abhyankar first proved this theorem in 1966.
Classes de Chern et classes de cycles en cohomologie de Hodge-Witt logarithmique
Let k be a perfect field of characteristic p > 0 . For every smooth k-scheme X , we define a theory of Chem classes and cycle classes with value in thé étale cohorology groups " ( X ^ ,W n ), whBre WExpand
Resolution Of Singularities Of Embedded Algebraic Surfaces
0 Introduction.- 1. Local Theory.- 1 Terminology and preliminaries.- 2 Resolvers and principalizers.- 3 Dominant character of a normal sequence.- 4 Unramified local extensions.- 5 Main results.- 2.Expand
Triangulated categories of motives over a field
3 Motivic complexes. 12 3.1 Nisnevich sheaves with transfers and the category DM − (k). . 12 3.2 The embedding theorem. . . . . . . . . . . . . . . . . . . . . . 20 3.3 Etale sheaves with transfers.Expand
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