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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Vector bundles on complex projective spaces and systems of partial differential equations. I
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by Peter F. Stiller PDF
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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Additional Information
  • © Copyright 1986 American Mathematical Society
  • 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