#### Volume 19, issue 1 (2015)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement Author Index To Appear ISSN (electronic): 1364-0380 ISSN (print): 1465-3060 Other MSP Journals
On the construction problem for Hodge numbers

### Stefan Schreieder

Geometry & Topology 19 (2015) 295–342
##### Abstract

For any symmetric collection ${\left({h}^{p,q}\right)}_{p+q=k}$ of natural numbers, we construct a smooth complex projective variety $X$ whose weight-$k$ Hodge structure has Hodge numbers ${h}^{p,q}\left(X\right)={h}^{p,q}$; if $k=2m$ is even, then we have to impose that ${h}^{m,m}$ is bigger than some quadratic bound in $m$. Combining these results for different weights, we solve the construction problem for the truncated Hodge diamond under two additional assumptions. Our results lead to a complete classification of all nontrivial dominations among Hodge numbers of Kähler manifolds.

##### Keywords
construction problem, Kähler geometry, Hodge numbers
##### Mathematical Subject Classification 2010
Primary: 32Q15
Secondary: 14C30, 51M15