JournalscmhVol. 88, No. 2pp. 449–468

Remarks on the Lefschetz standard conjecture and hyperkähler varieties

  • François Charles

    Université de Rennes 1, France
Remarks on the Lefschetz standard conjecture and hyperkähler  varieties cover

Abstract

We study the Lefschetz standard conjecture on a smooth complex projective variety XX. In degree 22, we reduce it to a local statement concerning local deformations of vector bundles on XX. When XX is hyperkähler, we show that the existence of nontrivial deformations of stable hyperholomorphic bundles implies the Lefschetz standard conjecture in codimension 22.

Cite this article

François Charles, Remarks on the Lefschetz standard conjecture and hyperkähler varieties. Comment. Math. Helv. 88 (2013), no. 2, pp. 449–468

DOI 10.4171/CMH/291