Infinitely generated Lawson homology groups on some rational projective varieties
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- by Wenchuan Hu PDF
- Proc. Amer. Math. Soc. 137 (2009), 2251-2264
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
- Email: wenchuan@math.mit.edu
- 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
- © Copyright 2008 by the author
- Journal: Proc. Amer. Math. Soc. 137 (2009), 2251-2264
- MSC (2000): Primary 14F43; Secondary 55Pxx
- DOI: https://doi.org/10.1090/S0002-9939-08-09798-0
- MathSciNet review: 2495258