On the Hodge conjecture for $q$-complete manifolds

Franc Forstneric; Jaka Smrekar; Alexandre Sukhov

doi:10.2140/gt.2016.20.353

On the Hodge conjecture for $q$-complete manifolds

Algebraic Geometry 2016-03-09 v2 Complex Variables

Authors: Franc Forstneric , Jaka Smrekar , Alexandre Sukhov

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Abstract

We establish the Hodge conjecture for the top dimensional cohomology group with integer coefficients of any $q$ -complete complex manifold $X$ with $q<\dim X$ . This holds in particular for the complement $X=\mathbb{C}\mathbb{P}^n\setminus A$ of any complex projective manifold defined by $q<n$ independent equations.

Keywords

Hodge conjecture q-complete manifold top cohomology complex manifold projective manifold complement integer coefficients

Cite

@article{arxiv.1404.2225,
  title  = {On the Hodge conjecture for $q$-complete manifolds},
  author = {Franc Forstneric and Jaka Smrekar and Alexandre Sukhov},
  journal= {arXiv preprint arXiv:1404.2225},
  year   = {2016}
}

Comments

In this version we improved most of the main results, showing that the analytic cycles representing the top dimensional cohomology classes of a $q$-complete complex manifold can be chosen to consist of holomorphic images of the ball (instead of ellipsoids that were used in Version 1)

On the Hodge conjecture for $q$-complete manifolds

Abstract

Keywords

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