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

Stiller, Peter F.

doi:10.1090/S0002-9947-1986-0860379-0

Vector bundles on complex projective spaces and systems of partial differential equations. I
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Trans. Amer. Math. Soc. 298 (1986), 537-548 Request permission

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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