zbMATH — the first resource for mathematics

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.
14C15 (Equivariant) Chow groups and rings; motives
14M10 Complete intersections
Full Text: DOI EuDML arXiv
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.