Vector Bundles on Complex Projective Spaces and Systems of Partial Differential Equations. I
- 1 December 1986
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 298 (2) , 537-548
- https://doi.org/10.2307/2000635
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.Keywords
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