On the construction problem for Hodge numbers

Abstract

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 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 Kaehler manifolds.

34 pages; final version, to appear in Geometry & Topology

References in corpus (1)

• Construction and examples of higher-dimensional modular Calabi-Yau manifolds

Cited by in corpus (9)

• On the Chow ring of Cynk-Hulek Calabi-Yau varieties and Schreieder varieties
• Multiplicative Chow-Künneth decompositions and varieties of cohomological K3 type
• Kaehler structures on spin 6-manifolds
• The construction problem for Hodge numbers modulo an integer
• The construction problem for Hodge numbers modulo an integer in positive characteristic
• Special Values of Motivic $L$-Functions and Zeta-Polynomials for Symmetric Powers of Elliptic Curves
• Hodge Groups of Hodge Structures with Hodge Numbers $(n,0,\dots ,0,n)$
• Chow motives associated to certain algebraic Hecke characters
• Some explicit elliptic modular surfaces