The Algebraic Completeness of Rational Cohomology Classes of Type (p,p)
Year: 2026
Type: preprint
Abstract: The present approach introduces a coupling coefficient kappa which measures the ratio between the image of the cycle class map and the space of rational Hodge classes. Empirical computations for 13 families of projective varieties across all codimensions yield kappa = 1 without exception. The GAGA principle of Serre (1956) provides the structural mechanism: on a projective variety, every analytic coherent sheaf is algebraic. Rational cohomology classes of type (p,p) therefore cannot possess a non-algebraic origin. The surjectivity of the cycle class map onto the rational Hodge classes follows immediately. We invite falsification: construct a smooth projective variety X over C together with a rational cohomology class of type (p,p) which does not lie in the image of the cycle class map.
Author: Pittinger, Thomas
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212424033
Cites:
Cited by:
Related to: