The Michigan Mathematical Journal

Birational invariants defined by Lawson homology

Wenchuan Hu

Full-text: Open access

Article information

Source
Michigan Math. J. Volume 60, Issue 2 (2011), 331-354.

Dates
First available in Project Euclid: 14 July 2011

Permanent link to this document
http://projecteuclid.org/euclid.mmj/1310667980

Digital Object Identifier
doi:10.1307/mmj/1310667980

Mathematical Reviews number (MathSciNet)
MR2825266

Zentralblatt MATH identifier
05938568

Subjects
Primary: 14F43: Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)
Secondary: 14E05: Rational and birational maps

Citation

Hu, Wenchuan. Birational invariants defined by Lawson homology. Michigan Math. J. 60 (2011), no. 2, 331--354. doi:10.1307/mmj/1310667980. http://projecteuclid.org/euclid.mmj/1310667980.


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References

  • H. Clemens, Homological equivalence, modulo algebraic equivalence, is not finitely generated, Inst. Hautes Études Sci. Publ. Math. 58 (1983), 19–38.
  • A. Dold and R. Thom, Quasifaserungen und unendliche symmetrische Produkte, Ann. of Math. (2) 67 (1958) 239–281.
  • E. Friedlander, Algebraic cycles, Chow varieties, and Lawson homology, Compositio Math. 77 (1991), 55–93.
  • –––, Filtrations on algebraic cycles and homology, Ann. Sci. École Norm. Sup. (4) 28 (1995), 317–343.
  • E. Friedlander and O. Gabber, Cycle spaces and intersection theory, Topological methods in modern mathematics (Stony Brook, 1991), pp. 325–370, Publish or Perish, Houston, TX, 1993.
  • E. Friedlander, C. Haesemeyer, and M. Walker, Techniques, computations, and conjectures for semi-topological $K$-theory, Math. Ann. 330 (2004), 759–807.
  • E. Friedlander and B. Lawson Jr., A theory of algebraic cocycles, Ann. of Math. (2) 136 (1992), 361–428.
  • E. Friedlander and B. Mazur, Filtrations on the homology of algebraic varieties. With an appendix by Daniel Quillen, Mem. Amer. Math. Soc. 110 (1994).
  • P. Griffiths, On the periods of certain rational integrals I, II, Ann. of Math. (2) 90 (1969), 460–495, 496–541.
  • P. Griffiths and J. Harris, Principles of algebraic geometry, Wiley, New York, 1994.
  • A. Grothendieck, Standard conjectures on algebraic cycles, Algebraic geometry (Bombay, 1968), pp. 193–199, Oxford Univ. Press, London, 1969.
  • H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II, Ann. of Math. (2) 79 (1964), 109–203, 205–326.
  • W. Hu, Generalized Abel–Jacobi map on Lawson homology, Amer. J. Math. 131 (2009), 1241–1260.
  • H. B. Lawson Jr., Algebraic cycles and homotopy theory, Ann. of Math. (2) 129 (1989), 253–291.
  • –––, Spaces of algebraic cycles, Surveys in differential geometry (Cambridge, 1993), vol. 2, pp. 137–213, International Press, Cambridge, MA, 1995.
  • J. D. Lewis, A survey of the Hodge conjecture, 2nd ed., CRM Monogr. Ser., 10, Amer. Math. Soc., Providence, RI, 1999.
  • D. I. Lieberman, Numerical and homological equivalence of algebraic cycles on Hodge manifolds, Amer. J. Math. 90 (1968), 366–374.
  • P. Lima-Filho, Lawson homology for quasiprojective varieties, Compositio Math. 84 (1992), 1–23.
  • –––, On the generalized cycle map, J. Differential Geom. 38 (1993), 105–129.
  • C. Peters, Lawson homology for varieties with small Chow groups and the induced filtration on the Griffiths groups, Math. Z. 234 (2000), 209–223.
  • M. Voineagu, Semi-topological $K$-theory for certain projective varieties, J. Pure Appl. Algebra 212 (2008), 1960–1983.
  • C. Voisin, Hodge theory and complex algebraic geometry, II (L. Schneps, transl.), Cambridge Stud. Adv. Math., 77, Cambridge Univ. Press, Cambridge, 2003.
  • M. E. Walker, The morphic Abel–Jacobi map, Compositio Math. 143 (2007), 909–944.