Remarks on the Lefschetz standard conjecture and hyperkähler varieties

2010/02/26 by François Charles, Charles, François
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · doi:10.48550/arxiv.1002.5011

openalex publication_date 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Lefschetz standard conjecture on a smooth complex projective variety X. In degree 2, we reduce it to a local statement concerning deformations of vector bundles on X. When X is hyperkähler, we show that the existence of nontrivial deformations of stable hyperholomorphic bundles implies the Lefschetz standard conjecture in codimension 2.

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