On the construction problem for Hodge numbers

Schreieder, Stefan

doi:10.2140/gt.2015.19.295

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On the construction problem for Hodge numbers

Stefan Schreieder

Geometry & Topology 19 (2015) 295–342

DOI: 10.2140/gt.2015.19.295

Abstract

For any symmetric collection ${(h^{p, q})}_{p + q = k}$ of natural numbers, we construct a smooth complex projective variety $X$ whose weight- $k$ Hodge structure has Hodge numbers $h^{p, q} (X) = h^{p, q}$ ; if $k = 2 m$ 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

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/

Volume 19, issue 1 (2015)