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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Algebraic cycles of a fixed degree


Author: Wenchuan Hu
Journal: Proc. Amer. Math. Soc. 138 (2010), 2365-2373
MSC (2010): Primary 14C25; Secondary 14F35, 14F45
Published electronically: February 25, 2010
MathSciNet review: 2607865
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Abstract: In this paper, the homotopy groups of Chow variety $ C_{p,d}(\mathbb{P}^n)$ of effective $ p$-cycles of degree $ d$ are proved to be stable in the sense that $ p$ or $ n$ increases. We also obtain a negative answer to a question by Lawson and Michelsohn on homotopy groups for the space of degree two cycles.


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Additional Information

Wenchuan Hu
Affiliation: Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540
Email: wenchuan@math.ias.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10311-6
PII: S 0002-9939(10)10311-6
Keywords: Algebraic cycle, Chow variety, homotopy group
Received by editor(s): October 16, 2009
Received by editor(s) in revised form: November 27, 2009
Published electronically: February 25, 2010
Additional Notes: This material is based upon work supported by the NSF under agreement No. DMS-0635607.
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.