Birkhoff-Grothendieck theorem
- Birkhoff-Grothendieck theorem
In mathematics, the Birkhoff-Grothendieck theorem concerns properties of vector bundles over complex projective space . It reduces every vector bundle over into direct sum of tautological line bundles, which enables one to deal with the bundle in a practical way. More precisely, the statement of the theorem is as the following.
Every holomorphic vector bundle on can be written as a direct sum of line bundles:
:
References
*citation
first1 = Alexander | last = Grothendieck | authorlink = Alexander Grothendieck
title = Sur la classification des fibres holomorphes sur la sphere de Riemann
journal = American Journal of Mathematics | volume = 79 | year = 1957 | pages = 121•138
doi = 10.2307/2372388.
*citation
first1 = C. | last1 = Okonek
first2 = M. | last2 = Schneider
first3 = H. | last3 = Spindler
title = Vector bundles on complex projective spaces
series = Progress in Mathematics | publisher = Birkhäuser | year = 1980.
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