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arXiv 1908.115732019-08math.DG

Geometric Methods in Partial Differential Equations

Ahmed Sebbar, Daniele Struppa, Oumar Wone

备注：: arXiv admin note: text overlap with arXiv:1910.12497

英文摘要：

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.

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