Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

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

  • [CW] W-L. Chow and B. L. van der Waerden, Zur algebraischen Geometrie. IX (German). Math. Ann. 113 (1937), no. 1, 692-704. MR 1513117
  • [F] E. Friedlander, Algebraic cycles, Chow varieties, and Lawson homology. Compositio Math. 77 (1991), no. 1, 55-93. MR 1091892 (92a:14005)
  • [GH] P. Griffiths and J. Harris, Principles of algebraic geometry. Reprint of the 1978 original. Wiley Classics Library. John Wiley & Sons, Inc., New York, 1994. MR 1288523 (95d:14001)
  • [L1] H. B. Lawson, Algebraic cycles and homotopy theory. Ann. of Math. (2) 129 (1989), 253-291. MR 986794 (90h:14008)
  • [L2] H. B. Lawson, Spaces of algebraic cycles. pp. 137-213 in Surveys in Differential Geometry, vol. 2, International Press, Cambridge, MA, 1995. MR 1375256 (97m:14006)
  • [LM] H. B. Lawson and M. L. Michelsohn, Algebraic cycles, Bott periodicity, and the Chern characteristic map. The mathematical heritage of Hermann Weyl (Durham, NC, 1987), 241-263, Proc. Sympos. Pure Math., 48, Amer. Math. Soc., Providence, RI, 1988. MR 974339 (90d:14010)
  • [M] I. G. Macdonald, The Poincaré polynomial of a symmetric product. Proc. Cambridge Philos. Soc. 58 (1962), 563-568. MR 0143204 (26:764)
  • [W] George W. Whitehead, Elements of homotopy theory. Graduate Texts in Mathematics, 61. Springer-Verlag, New York-Berlin, 1978. MR 516508 (80b:55001)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 14C25, 14F35, 14F45

Retrieve articles in all journals with MSC (2010): 14C25, 14F35, 14F45

Additional Information

Wenchuan Hu
Affiliation: Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540

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.

American Mathematical Society