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Hermitian vector bundles and the equidistribution of the zeroes of their holomorphic sections
Open accessAbstract
At present a great deal is known about the value distribution of systems of meromorphic functions on an open Riemann surface. One has the beautiful results of Picard, E. Borel, Nevanlinna, Ahlfors, H. and J. Weyl and many others to point to. (See [1], [2].) The aim of this paper is to make the initial step towards an n-dimensional analogue of this theory. A natural general setting for the value distribution theory is the following one. We consider a complex n-manifold X and a holomorphic vector bundle E over X whose fiber dimension equals the dimension of X and wish to study the zero-sets of holomorphic sections of E. When X is compact (and without boundary) then it is well-known that if the zeroes of any continuous section are counted properly then the algebraic sum of these zero-points is independent of the section and is given by the integral of the nth Chern(2) class of E over X: Thus we have zeroes of s = | cn(E), (1.1) Number of J x
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Cited by
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Simon, B. (1983) · Physical Review Letters · doi:10.1103/physrevlett.51.2167 · Cited by 1,919
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Donaldson, S. K. (1985) · Proceedings of the London Mathematical Society · doi:10.1112/plms/s3-50.1.1 · Cited by 1,047
Zanardi, P., & Rasetti, M. (1999) · Physics Letters A · doi:10.1016/s0375-9601(99)00803-8 · Cited by 1,006
Geometric phase from Aharonov–Bohm to Pancharatnam–Berry and beyond
Cohen, E., Larocque, H., Bouchard, F., Nejadsattari, F., Gefen, Y., & Karimi, E. (2019) · Nature Reviews Physics · doi:10.1038/s42254-019-0071-1 · Cited by 305
Chern, S. S. (1966) · Bulletin of the American Mathematical Society · doi:10.1090/s0002-9904-1966-11473-8 · Cited by 159
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Metadata
- Authors
- Bott, R., & Chern, S. S.
- Venue
- Acta Mathematica
- Publisher
- International Press of Boston
- Published
- 1965
- Volume
- 114
- Issue
- 0
- Pages
- 71-112
- ISSN
- 0001-5962 (ISSN-L)
- OpenAlex
- W2044356794
- Cited by
- 287
- References
- 0
- FWCI
- 4.08
- Type
- journal article
- Language
- en
- Open access
- bronze
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