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Enumerative geometry of triangles. III. (English) Zbl 0648.14031

The third part of this paper concludes the verification of Schubert’s enumerative calculus for triangles in \(P^ 2\). One proves that the ring \(A^{\bullet}(W^*)\) is generated by \(Pic(W^*)\) and that the graded components of \(A^{\bullet}(W^*)\) are free \({\mathbb{Z}}\)-modules of ranks 1, 7, 17, 22, 17, 7 and 1. In the final part of the paper one compares the results about \(W^*\) with those of Elencwajg and Le Barz about \(Hilb_ 3(P^ 2).\)
[See also the two preceding reviews.]
Reviewer: L.Bădescu

MSC:

14N10 Enumerative problems (combinatorial problems) in algebraic geometry
14C05 Parametrization (Chow and Hilbert schemes)
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References:

[1] Collino A. Fulton W. work in progress
[2] Elencwajg, G. and Le Barz, P. 1985.Détermination de Tanneau de Chow de Hilb3(P2), Vol. 301, 635–638. Paris: C.R. Acad. Sci. Sér. Math · Zbl 0597.14005
[3] Ellingsrud G., On the homology of the Hubert scheme of points in the plane 13 (1984)
[4] Fulton W., Intersection Theory, Ergibnisse der Mathematik 2 (1984) · Zbl 0541.14005
[5] DOI: 10.1080/00927877908822424 · Zbl 0435.14016
[6] DOI: 10.1080/00927878408823051 · Zbl 0648.14029
[7] DOI: 10.1080/00927878608823302 · Zbl 0648.14030
[8] Schubert H., Kalkül der abzählenden Geometrie (1979)
[9] DOI: 10.1007/BF01443470
[10] Serre J.P., A Course in Arithmetic 7 (1973) · Zbl 0256.12001
[11] Speiser, R. 1985. Enumerating contacts. Proc. Sympos.in Pure Math. 1985. Brunswick: Proc. of AMS Summer Inst. to appear · Zbl 0673.14027
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