On the tangent spaces of Chow groups of certain projective hypersurfaces

Ching, Avery

doi:10.1090/S0002-9939-03-07154-5

On the tangent spaces of Chow groups of certain projective hypersurfaces
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Proc. Amer. Math. Soc. 132 (2004), 325-331 Request permission

Abstract:

In this paper, the Chow groups of projective hypersurfaces are studied. We will prove that if the degree of the hypersurface is sufficiently high, its Chow group is “small” in the sense that its formal tangent space vanishes. Then, we will give an example in which the formal tangent space is infinite dimensional.

References

Pierre Deligne, James S. Milne, Arthur Ogus, and Kuang-yen Shih, Hodge cycles, motives, and Shimura varieties, Lecture Notes in Mathematics, vol. 900, Springer-Verlag, Berlin-New York, 1982. MR 654325, DOI 10.1007/978-3-540-38955-2
Hélène Esnault and Kapil H. Paranjape, Remarks on absolute de Rham and absolute Hodge cycles, C. R. Acad. Sci. Paris Sér. I Math. 319 (1994), no. 1, 67–72 (English, with English and French summaries). MR 1285900
Mark L. Green, Griffiths’ infinitesimal invariant and the Abel-Jacobi map, J. Differential Geom. 29 (1989), no. 3, 545–555. MR 992330
Green, M. L., Banff lecture notes, 1998
Mark L. Green, Infinitesimal methods in Hodge theory, Algebraic cycles and Hodge theory (Torino, 1993) Lecture Notes in Math., vol. 1594, Springer, Berlin, 1994, pp. 1–92. MR 1335239, DOI 10.1007/978-3-540-49046-3_{1}
Phillip A. Griffiths, On the periods of certain rational integrals. I, II, Ann. of Math. (2) 90 (1969), 460-495; ibid. (2) 90 (1969), 496–541. MR 0260733, DOI 10.2307/1970746
Phillip Griffiths and Joe Harris, On the Noether-Lefschetz theorem and some remarks on codimension-two cycles, Math. Ann. 271 (1985), no. 1, 31–51. MR 779603, DOI 10.1007/BF01455794
Wilberd van der Kallen, Generators and relations in algebraic $K$-theory, Proceedings of the International Congress of Mathematicians (Helsinki, 1978) Acad. Sci. Fennica, Helsinki, 1980, pp. 305–310. MR 562620
Kazuhiro Konno, On the variational Torelli problem for complete intersections, Compositio Math. 78 (1991), no. 3, 271–296. MR 1106298
Daniel Quillen, Higher algebraic $K$-theory. I, Algebraic $K$-theory, I: Higher $K$-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972) Lecture Notes in Math., Vol. 341, Springer, Berlin, 1973, pp. 85–147. MR 0338129