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