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Lefschetz classes on projective varieties


Authors: June Huh and Botong Wang
Journal: Proc. Amer. Math. Soc. 145 (2017), 4629-4637
MSC (2010): Primary 14C25; Secondary 14C20, 14M15
DOI: https://doi.org/10.1090/proc/13757
Published electronically: July 28, 2017
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Abstract: 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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Additional Information

June Huh
Affiliation: Institute for Advanced Study, Fuld Hall, 1 Einstein Drive, Princeton, New Jersey 08540
Email: huh@princeton.edu

Botong Wang
Affiliation: University of Wisconsin-Madison, Van Vleck Hall, 480 Lincoln Drive, Madison, Wisconsin 53706
Email: bwang274@wisc.edu

DOI: https://doi.org/10.1090/proc/13757
Received by editor(s): November 30, 2016
Published electronically: July 28, 2017
Communicated by: Lev Borisov
Article copyright: © Copyright 2017 American Mathematical Society

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