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Blowing up Chern Classes

Published online by Cambridge University Press:  24 October 2008

I. R. Porteous
I. R. Porteous
Affiliation:
Trinity CollegeCambridge
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Extract

The behaviour of the Chern classes or of the canonical classes of an algebraic variety under a dilatation has been studied by several authors (Todd (8)–(11), Segre (5), van de Ven (12)). This problem is of interest since a dilatation is the simplest form of birational transformation which does not preserve the underlying topological structure of the algebraic variety. A relation between the Chern classes of the variety obtained by dilatation of a subvariety and the Chern classes of the original variety has been conjectured by the authors cited above but a complete proof of this relation is not in the literature.

Type
Articles
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 56 , Issue 2 , April 1960 , pp. 118 - 124
Copyright
Copyright © Cambridge Philosophical Society 1960

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References

REFERENCES

(1)Borel, A., and Serre, J. P., Le théorème de Riemann-Roch. Bull. Soc. Math. Fr. 86 (1958), 97–136.CrossRefGoogle Scholar
(2)Grothendieck, A., La théorie des classes de Chern. Bull. Soc. Math. Fr. 86 (1958), 137–54.CrossRefGoogle Scholar
(3)Northcott, D. G., On the algebraic foundations of the theory of local dilatation. Proc.Lond. Math. Soc. (3), 6 (1956), 267–85.CrossRefGoogle Scholar
(4)Segre, B., Dilatazioni e comportamenti associati nel campo analitico. Rend. Circ. mat. Palermo, (2), 1 (1952), 373–9.CrossRefGoogle Scholar
(5)Segre, B., Dilatazioni e varietà canoniche sulla varietà algebriche. Ann. Mat. pura appl. (4), 37 (1954), 139–55.CrossRefGoogle Scholar
(6)Séminaire, Chevailey, 26 année. Anneaux de Chow et applications (Paris, 1958).Google Scholar
(7)Serre, J. P., Faisceaux algébriques cohérents. Ann. Math. 61 (1955), 197–278.CrossRefGoogle Scholar
(8)Todd, J. A., Birational transformations with isolated fundamental points. Proc. Edinb. Math. Soc. (2), 5 (1938), 117–24.CrossRefGoogle Scholar
(9)Todd, J. A., Birational transformations possessing fundamental curves. Proc. Camb. Phil. Soc. 34 (1938), 144–55.CrossRefGoogle Scholar
(10)Todd, J. A., Birational transformations with a fundamental surface. Proc. Lond. Math. Soc. (2), 47 (1941), 81–100.Google Scholar
(11)Todd, J. A., Canonical systems on algebraic varieties. Bol. Soc. Mat. Mexicana, (2), 2 (1957), 26–44.Google Scholar
(12)van de Ven, A. J. H. M., Characteristic classes and monoidal transformations. Indag. math. 18 (1956), 571–8.CrossRefGoogle Scholar
(13)Washnitzer, G., Geometric syzygies. Amer. J. Math. 81 (1959), 171–248.CrossRefGoogle Scholar