On the construction problem for Hodge numbers

Schreieder, Stefan¹

¹ Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany, Mathematisches Institut, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany

Geometry & topology, Tome 19 (2015) no. 1, pp. 295-342.

Résumé

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.

Détail

DOI : 10.2140/gt.2015.19.295

Classification : 32Q15, 14C30, 51M15
Keywords: construction problem, Kähler geometry, Hodge numbers

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