Title

Geometric Methods in Partial Differential Equations

Document Type

Article

Publication Date

11-22-2021

Abstract

We study the interplay between geometry and partial differential equations. We show how the fundamental ideas we use require the ability to correctly calculate the dimensions of spaces associated to the varieties of zeros of the symbols of those differential equations. This brings to the center of the analysis several classical results from algebraic geometry, including the Cayley-Bacharach theorem and some of its variants as Serret’s theorem, and the Brill-Noether Restsatz theorem.

Comments

This article was originally published in Milan Journal of Mathematics, volume 89, in 2021. https://doi.org/10.1007/s00032-021-00336-9

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Peer Reviewed

1

Copyright

Springer

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