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Excess intersections and a correspondence principle. (English) Zbl 0733.14002
This paper elucidates the relation between two types of excess intersections. On the one hand we have special techniques applicable in special situations such as projective space or hypersurfaces developed by Vogel, Stückrad, Brownawell, Philippon etc. On the other hand, we have the abstract theory of Fulton and MacPherson which applies in general. Before this paper, it was not at all clear what the relation was between these two approaches. Now, fortunately, the author has shown how they are related.

MSC:
14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
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[1] Ådlandsvik, B.: Joins and higher secant varieties. Math. Scand.61, 213-222 (1987) · Zbl 0657.14034
[2] Baker, H.F.: Principles of geometry, vol. VI. Cambridge: Cambridge Univ. Press 1933 · Zbl 0008.21906
[3] Brownawell, W.D.: Note on a paper of P. Philippon. Michigan Math. J.34, 461-464 (1987) · Zbl 0634.14002 · doi:10.1307/mmj/1029003625
[4] Fiorentini, M., Lascu, A.T.: Una formula di geometria numerativa. Ann. Univ. Ferrara27, 201-227 (1981) · Zbl 0513.14036
[5] Flenner, H., Vogel, W.: Connectivity and its applications to improper intersections inP n . Preprint no. 53. Göttingen 1988
[6] Fulton, W.: Intersection theory. (Ergebnisse der Math. 3, Bd. 2). Berlin-Heidelberg-New York: Springer 1984 · Zbl 0541.14005
[7] Fulton, W.: Algebraic refined intersections. (Notes for Math., 271). Brown University, Providence R.I., November 1986
[8] Fulton, W., Lazarsfeld, R.: Connectivity and its applications in algebraic geometry. In: Libgober, A., Wagreich, P. (eds.) Algebraic Geometry. Proceedings, University of Illinois at Chicago Circle 1980. (Lecture Notes in Math., vol. 862, pp. 26-92). Berlin-Heidelberg-New York: Springer 1981 · Zbl 0484.14005
[9] Gastel, L.J. van: Excess intersections. Thesis, Rijksuniversiteit Utrecht, March 1989
[10] Hartshorne, R.: Algebraic geometry. (Graduate Texts in Math., vol. 52). Berlin-Heidelberg-New York: Springer 1977 · Zbl 0367.14001
[11] Holme, A.: Embedding obstructions for singular varieties inP n . Acta. Math.135, 155-185 (1975) · Zbl 0339.14007 · doi:10.1007/BF02392018
[12] Johnson, K. W.: Immersion and embedding of projective varieties. Acta Math.140, 49-74 (1978) · Zbl 0373.14005 · doi:10.1007/BF02392303
[13] Kirby, D.: On Bézout’s theorem. Q. J. Math. Oxford39, 469-481 (1988) · Zbl 0685.14005 · doi:10.1093/qmath/39.4.469
[14] Peters, C.A.M., Simonis, J.: A secant formula. Q. J. Math. Oxford27, 181-189 (1976) · Zbl 0334.14028 · doi:10.1093/qmath/27.2.181
[15] Philippon, P.: Lemmes de zéros dans les groupes algébriques commutatifs. Bull. Soc. Math. France114, 355-383 (1986) · Zbl 0617.14001
[16] Pieri, M.: Formule di coincidenza per le serie algebriche ? n di coppie di punti dello spazio an dimensioni. Rend. Circ. Mat. Palermo5, 252-268 (1891) · JFM 23.0700.02 · doi:10.1007/BF03015699
[17] Samuel, P.: La notion de multiplicité en algèbre et en géométrie algébrique. J. Math. Pures Appl.30, 159-274 (1951) · Zbl 0044.02701
[18] Stückrad, J., Vogel, W.: An algebraic approach to the intersection theory. In: Geramita, A.V. (ed.) The Curves Seminar at Queen’s University, vol. II. Queen’s Papers Pure Appl. Math. 61, pp. 1-32. Kingston, Ontario 1982
[19] Vogel, W.: Results on Bézout’s theorem. (Tata Lect. Notes, vol. 74). Berlin-Heidelberg-New York: Springer 1984
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