Summary
New techniques are developed, based on the consideration of the projective bundle associated with a direct sum of two vector bundles, to give a simpler solution of the problem of blowing up Chern classes which was previously solved by Porteous[12] using the Grothendieck Riemann-Roch theorem.
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A. Borel -F. Hirzebruch,Characteristic classes and homogeneous spaces, I, II, III, Am. Journal of Math.,80 (1958), pp. 458–538;81 (1959), pp. 315–382;82 (1960), pp. 491–504.
A. Borel -J.-P. Serre, Le théoreme de Riemann-Roch, Bull. Soc. Math. de France,86 (1958), pp. 97–136.
N. Bourbaki,Eléments de Mathematique, vol. XXXIII and XXXVI.
SeminaireC. Chevalley,Anneaux de Chow et applications, Secretariat mathématique, 11 Rue Pierre Curie, Paris 5e, 1958.
Gh. Galbura, Sui covarianti di immersione, Rend. di Mat.,25 (1966), pp. 239–247 (Castelnuovo centenary volume).
Gh. Galbura -A. T. Lascu, Eclatement des classes de Chern d'une variété algébrique, Rev. Rom. Math. Pures et Appl.,12 (1967), pp. 1255–1258.
A. Grothendieck, La théorie des classes de Chern, Bull. Soc. Math. de France,86 (1958), pp. 137–159.
F. Hirzebruch,Topological methods in algebraic geometry, Grundlehren der Math. Wissenschaften,131 (1966).
S. A. Ilori - A. W. Ingleton - A. T. Lascu,On a formula of D. B. Scott (in preparation) (to appear in J. London Math. Soc.).
A. W. Ingleton -D. B. Scott,The tangent direction bundle of an algebraic variety and generalized Jacobians of linear systems, Annali di Mat., (4),56 (1961), pp. 359–374.
J.-P. Jouanolou, Riemann-Roch sans dénominateurs, Inventiones Math.,11 (1970), pp. 15–26.
I. R. Porteous,Blowing up Chern classes, Proc. Cambridge Phil. Soc.,56 (1960), pp. 118–124.
I. R. Porteous,Simple Singularities of Maps, inProc. Liverpool Singularities Symposium I, Springer Lecture Notes in Mathematics, vol. 192.
D. B. Scott,Natural lifts and the covariant systems of Todd, J. London Math. Soc., (2),1 (1969), pp. 709–718.
D. B. Scott,A topological approach to branch and double curves of correspondences between algebraic surfaces, Convegno Internazionale Enriques, Milano, 1971.
B. Segre, Nuovi metodi e risultati nella geometria sulle varietà algebriche, Annali di Mat., (4),35 (1953), pp. 1–127.
B. Segre, Dilatazioni e varietà canoniche sulle varietà algebriche, Annali di Mat., (4),37 (1954), pp. 139–155.
J. A. Todd,Birational transformations with isolated fundamental points, Proc. Edinburgh Math. Soc., (2),5 (1938), pp. 117–124.
J. A. Todd,Birational transformations possessing fundamental curves, Proc. Cambridge Phil. Soc.,34 (1938), pp. 144–155.
J. A. Todd,Invariant and covariant systems on an algebraic variety, Proc. London Math. Soc., (2),46 (1940), pp. 199–230.
J. A. Todd,Birational transformations with a fundamental surface, Proc. London Math. Soc., (2),47 (1941), pp. 81–100.
J. A. Todd,Canonical systems on algebraic varieties, Boletin de la Sociedad Matematica Mexicana (1957), pp. 38–44.
A. J. H. M. Van de Ven,Characteristic classes and monoidal transformations, Indag. Math.,18 (1956), pp. 571–578.
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Dedicated to ProfessorBeniamino Segre
Entrata in Redazione il 2 aprile 1973.
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Lascu, A.T., Scott, D.B. An algebraic correspondence with applications to projective bundles and blowing up Chern classes. Annali di Matematica 102, 1–36 (1975). https://doi.org/10.1007/BF02410592
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DOI: https://doi.org/10.1007/BF02410592