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Complete intersections and rational equivalence. (English) Zbl 0854.14003
In this paper the author gives a new criterion (and consequence of it) for rational equivalence of cycles on a projective variety over an algebraically closed field.
MSC:
14C15 (Equivariant) Chow groups and rings; motives
14M10 Complete intersections
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References:
[1] Akizuki, Y.: Theorems of Bertini on linear systems. J. Math. Soc. Jpn.3, 170–180 (1951) · Zbl 0043.36302
[2] Baldassari, M.: Algebraic Varieties. (Ergebnisse der Mathematik) Berlin Heidelberg New York, Springer 1956 · Zbl 0075.15901
[3] Barlow, R.: Rational equivalence of zero-cycles for some more surfaces withp g=0. Invent. Math.79, 303–308 (1985) · Zbl 0584.14002
[4] Bloch, S.: Lectures on Algebraic Cycles. (Duke University Math. Series IV) Durham, NC: Duke University 1980 · Zbl 0436.14003
[5] Bloch, S.: Algebraic cycles and values of L-functions. J. Reine Angew. Math.350, 94–108 (1984) · Zbl 0527.14008
[6] Bloch, S., Kas, A. and Lieberman, D.: Zero cycles on surfaces withp g=0. Compositio Math.33, 135–145 (1976) · Zbl 0337.14006
[7] Bombieri, E.: Canonical models of surfaces of general type. Publ. Math IHES42, 171–220 (1973) · Zbl 0259.14005
[8] Donaldson, S. K.: Instantons in Yang-Mills theory. In: Interactions between particle physics and mathematics, pp. 59–75, Oxford: Oxford University Press 1989
[9] Fulton, W.: Intersection Theory. (Ergebnisse der Mathematik) Berlin Heidelberg New York: Springer 1984 · Zbl 0541.14005
[10] Griffiths, P.A.: An introduction to the theory of special divisors on algebraic curves. (CBMS regional conference series 44) Providence: American Mathematical Society 1980
[11] Griffiths, P. and Harris, J.: Residues and zero-cycles on algebraic varieties. Ann. Math.108, 461–505 (1978) · Zbl 0423.14001
[12] Inose, H. and Mizukami, M.: Rational equivalence of zero-cycles on some surfaces withp g=0. Math. Ann.244, 205–217 (1979) · Zbl 0444.14006
[13] Keum, J.H.: Some new surfaces of general type withp g=0. Preprint, University of Utah, Salt Lake City.
[14] Lewis, J.D.: A Survey of the Hodge Conjecture. Montreal: CRM publications 1991 · Zbl 0778.14002
[15] Mumford, D.: Rational equivalence of 0-cycles on surfaces. J. Math. Kyoto Univ.9, 195–204 (1969) · Zbl 0184.46603
[16] Murthy, M. and Swan, R.: Vector bundles over affine surfaces. Invent. Math.36, 125–165 (1976) · Zbl 0362.14006
[17] Roitman, A.A.: The torsion of the group of zero-cycles modulo rational equivalence. Ann. Math.111, 553–569 (1980) · Zbl 0504.14006
[18] Samuel, P.: Méthodes d’Algèbre Abstraite en Géométrie Algébrique. Berlin Heidelberg New York: Springer 1955
[19] Samuel, P.: Rational equivalence of arbitrary cycles. Am. J. Math.78, 383–400 (1956) · Zbl 0075.16002
[20] Severi, F.: Un’altra proprietà fondamentale delle serie di equivalenza sopra una superficia. Rend. Accad. Linc.21, 3–7 (1935) · Zbl 0011.17203
[21] Severi, F.: Serie, sistemi d’equivalenza e corrispondenze algebriche sulle varietà algebriche (vol 1). Rome: Cremonese 1942 · JFM 68.0365.01
[22] Shafarevich, I. R.: Basic Algebraic Geometry, Berlin Heidelberg New York: Springer 1974 · Zbl 0284.14001
[23] Todd, J. A.: Some group-theoretic considerations in algebraic geometry, Ann. Math.35, 702–704 (1934) · Zbl 0009.37104
[24] Van der Waerden, B.L.: Modern Algebra, volume II. New York: Unger 1950 · Zbl 0037.01903
[25] Voisin, C.: Sur les zéro-cycles de certaines hypersurfaces munies d’un automorphisme. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)19 473–492 (1992) · Zbl 0786.14006
[26] Xu, M.W.: The configuration of a finite set on surface. Preprint, MPI Bonn (1990)
[27] Zariski, O.: Algebraic Surfaces (Ergebnisse der Mathematik) Berlin Heidelberg New York: Springer 1971 · Zbl 0219.14020
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