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Proceedings of the American Mathematical Society

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



Infinitely generated Lawson homology groups on some rational projective varieties

Author: Wenchuan Hu
Journal: Proc. Amer. Math. Soc. 137 (2009), 2251-2264
MSC (2000): Primary 14F43; Secondary 55Pxx
Published electronically: December 23, 2008
MathSciNet review: 2495258
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Abstract: We construct rational projective 4-dimensional varieties with the property that certain Lawson homology groups tensored with $ { \mathbb{Q}}$ are infinite dimensional $ {\mathbb{Q}}$-vector spaces. More generally, for each pair of integers $ p$ and $ k$, with $ k\geq 0$, $ p>0$, we find a projective variety $ Y$ such that $ L_pH_{2p+k}(Y)$ is infinitely generated.

We also construct two singular rational projective 3-dimensional varieties $ Y$ and $ Y'$ with the same homeomorphism type but different Lawson homology groups; specifically, $ L_1H_3(Y)$ is not isomorphic to $ L_1H_3(Y')$ even up to torsion.

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Additional Information

Wenchuan Hu
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Building 2, Room 363B, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307

Keywords: Lawson homology, infinitely generated, non-homeomorphic invariants
Received by editor(s): April 2, 2007
Received by editor(s) in revised form: October 9, 2008
Published electronically: December 23, 2008
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2008 by the author