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Commentarii Mathematici Helvetici


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Volume 88, Issue 2, 2013, pp. 449–468
DOI: 10.4171/CMH/291

Published online: 2013-04-24

Remarks on the Lefschetz standard conjecture and hyperkähler varieties

François Charles[1]

(1) Université de Rennes 1, France

We study the Lefschetz standard conjecture on a smooth complex projective variety $X$. In degree $2$, we reduce it to a local statement concerning local 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 $2$.

Keywords: Algebraic cycles, holomorphic symplectic varieties, standard conjectures

Charles François: Remarks on the Lefschetz standard conjecture and hyperkähler varieties. Comment. Math. Helv. 88 (2013), 449-468. doi: 10.4171/CMH/291