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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Vector bundles on complex projective spaces and systems of partial differential equations. I


Author: Peter F. Stiller
Journal: Trans. Amer. Math. Soc. 298 (1986), 537-548
MSC: Primary 14F05; Secondary 32C35, 35E99
DOI: https://doi.org/10.1090/S0002-9947-1986-0860379-0
MathSciNet review: 860379
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Abstract: This paper establishes and investigates a relationship between the space of solutions of a system of constant coefficient partial differential equations and the cohomology ($ {H^1}$ in particular) of an associated vector bundle/reflexive sheaf on complex projective space. Using results of Grothendieck and Shatz on vector bundles over projective one-space, the case of partial differential equations in two variables is completely analyzed. The final section applies results about vector bundles on higher-dimensional projective spaces to the case of three or more variables.


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DOI: https://doi.org/10.1090/S0002-9947-1986-0860379-0
Article copyright: © Copyright 1986 American Mathematical Society