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Algebraic cycles of a fixed degree
Author(s):
Wenchuan
Hu
Journal:
Proc. Amer. Math. Soc.
138
(2010),
2365-2373.
MSC (2010):
Primary 14C25;
Secondary 14F35, 14F45
Posted:
February 25, 2010
MathSciNet review:
2607865
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Abstract:
In this paper, the homotopy groups of Chow variety  of effective  -cycles of degree  are proved to be stable in the sense that  or  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:
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- 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)
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- [L1]
- H. B. Lawson, Algebraic cycles and homotopy theory. Ann. of Math. (2) 129 (1989), 253-291. MR 986794 (90h:14008)
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- 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)
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- I. G. Macdonald, The Poincaré polynomial of a symmetric product. Proc. Cambridge Philos. Soc. 58 (1962), 563-568. MR 0143204 (26:764)
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- George W. Whitehead, Elements of homotopy theory. Graduate Texts in Mathematics, 61. Springer-Verlag, New York-Berlin, 1978. MR 516508 (80b:55001)
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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:
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
Posted:
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
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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