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Ranks of Chain Complexes Over the Complex Polynomial Ring

Published online by Cambridge University Press:  20 November 2018

Piotr M. Zelewski
Piotr M. Zelewski*
Affiliation:
Mathematics and Statistics, McMaster University, Hamilton, Ontario L8S 4K1
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Abstract

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Using LePotier's vanishing theorem, we establish a lower bound on the rank of nontrivial free differential complex in terms of the dimension of the support for its cohomology. Our bound specializes to the one predicted by the syzygy theorem of Evans and Griffith.

Keywords

13D2514C3014F05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 4 , 01 December 1991 , pp. 563 - 565
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Atiyah, M. F. and Bott, R., The moment map and equivariant cohomology, Topology 23 (1984), 1–28.Google Scholar
2. Carlsson, G., Free (Z/2)K actions and a problem in commutative algebra. Springer-Verlag Lecture Notes 1217, 1986, 79–84.Google Scholar
3. Evans, G. and Griffith, P., The syzygy problem, Annals of Math. 101 (1981), 323–334.Google Scholar
4. Halperin, S.: (Oral communication).Google Scholar
5. Hartshorne, R., Algebraic geometry. GTM-52, Springer-Verlag, 1977.Google Scholar
6. Kobayashi, S., Differential geometry of complex vector bundles. Princeton University Press, 1987.Google Scholar