Remarks on the Lefschetz standard conjecture and hyperkähler varieties

Details Remarks on the Lefschetz standard conjecture and hyperkähler varieties Remarks on the Lefschetz standard conjecture and hyperkähler varieties

2010-02-26

arxiv.org/abs/1002.5011v3

Mathematics

Algebraic Geometry

20 pages

Scientific paper

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 hyperk\"ahler, we show that the
existence of nontrivial deformations of stable hyperholomorphic bundles implies
the Lefschetz standard conjecture in codimension 2.

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