Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 14F43, 55Pxx

Retrieve articles in all journals with MSC (2000): 14F43, 55Pxx


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

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09798-0
PII: S 0002-9939(08)09798-0
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