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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
On the construction problem for Hodge numbers

Stefan Schreieder

Geometry & Topology 19 (2015) 295–342
Abstract

For any symmetric collection (hp,q)p+q=k of natural numbers, we construct a smooth complex projective variety X whose weight-k Hodge structure has Hodge numbers hp,q(X) = hp,q; if k = 2m is even, then we have to impose that hm,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
References
Publication
Received: 7 August 2013
Revised: 22 February 2014
Accepted: 17 April 2014
Published: 27 February 2015
Proposed: Lothar Göttsche
Seconded: Richard Thomas, Ciprian Manolescu
Authors
Stefan Schreieder
Max-Planck-Institut für Mathematik
Vivatsgasse 7
53111 Bonn
Germany
Mathematisches Institut
Universität Bonn
Endenicher Allee 60
53115 Bonn
Germany
http://www.math.uni-bonn.de/people/schreied/