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On q-th Derivative of Vector Bundles

Published online by Cambridge University Press:  22 January 2016

Akikuni Kato
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In the present note we shall be concerned with the improvement of fundamental definitions in higher order enumerative geometry which has been recently given by W. F. Pohl. Pohl’s definition of q-th derivative of vector bundle is very complicated. We shall give a simpler and more reasonable definition of the q-th derivative of vector bundle in terms of sheaf theory and simplify the proofs in [P]. We shall also give a definition of higher order singularity of map.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 29 , March 1967 , pp. 121 - 126
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1967

References

[B] Bourbaki, N.: Algèbre commutative, chap. 1, 2.Google Scholar
[G] Grothendieck, A.: Éléments de géométrie algébrique. Publ. Math. I.H.E.S.Google Scholar
[P] Pohl, W. F.: Differential geometry of higher order. Topology I, 169–211, 1962.Google Scholar