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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Lefschetz classes on projective varieties
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by June Huh and Botong Wang PDF
Proc. Amer. Math. Soc. 145 (2017), 4629-4637 Request permission

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
  • MR Author ID: 974745
  • Email: huh@princeton.edu
  • Botong Wang
  • Affiliation: University of Wisconsin-Madison, Van Vleck Hall, 480 Lincoln Drive, Madison, Wisconsin 53706
  • MR Author ID: 923993
  • Email: bwang274@wisc.edu
  • Received by editor(s): November 30, 2016
  • Published electronically: July 28, 2017
  • Communicated by: Lev Borisov
  • © Copyright 2017 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 4629-4637
  • MSC (2010): Primary 14C25; Secondary 14C20, 14M15
  • DOI: https://doi.org/10.1090/proc/13757
  • MathSciNet review: 3691982