Lefschetz classes on projective varieties

Lefschetz classes on projective varieties

The Lefschetz algebra L^*(X) of a smooth complex projective variety X is the subalgebra of the cohomology algebra of X generated by divisor classes. We construct smooth complex projective varieties whose Lefschetz algebras do not satisfy analogues of the hard Lefschetz theorem and Poincaré duality.

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Veröffentlicht in:Proceedings of the American Mathematical Society 2017-11, Vol.145 (11), p.4629-4637
Hauptverfasser: HUH, JUNE, WANG, BOTONG
Format: Artikel
Sprache:eng
Schlagworte:
A. ALGEBRA, NUMBER THEORY, AND COMBINATORICS
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Zusammenfassung:The Lefschetz algebra L^*(X) of a smooth complex projective variety X is the subalgebra of the cohomology algebra of X generated by divisor classes. We construct smooth complex projective varieties whose Lefschetz algebras do not satisfy analogues of the hard Lefschetz theorem and Poincaré duality.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/13757