English

The construction problem for Hodge numbers modulo an integer

Algebraic Geometry 2020-01-08 v2 Complex Variables Geometric Topology

Abstract

For any positive integer m and any dimension n, we show that any n-dimensional Hodge diamond with values in Z/mZ is attained by the Hodge numbers of an n-dimensional smooth complex projective variety. As a corollary, there are no polynomial relations among the Hodge numbers of n-dimensional smooth complex projective varieties besides the ones induced by the Hodge symmetries, which answers a question raised by Koll\'ar in 2012.

Keywords

Cite

@article{arxiv.1903.05430,
  title  = {The construction problem for Hodge numbers modulo an integer},
  author = {Matthias Paulsen and Stefan Schreieder},
  journal= {arXiv preprint arXiv:1903.05430},
  year   = {2020}
}

Comments

8 pages, to appear in Algebra & Number Theory

R2 v1 2026-06-23T08:06:49.938Z