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arXiv · 2302.02634

On the Schmidt--Kolchin conjecture on differentially homogeneous polynomials. Applications to (twisted) jet differentials on projective spaces

Antoine Etesse
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Abstract

The main goal of this paper is to prove the Schmidt--Kolchin conjecture. This conjecture says the following: the vector space of degree \(d\) differentially homogeneous polynomials in \((N+1)\) variables is of dimension \((N+1)^{d}\). Next, we establish a one-to-one correspondance between differentially homogeneous polynomials in \((N+1)\) variables, and twisted jet differentials on projective spaces. As a by-product of our study of differentially homogeneous polynomials, we are thus able to understand explicitly twisted jet differentials on projective spaces.

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BibTeXRIS

Antoine Etesse. 2023-02-06. On the Schmidt--Kolchin conjecture on differentially homogeneous polynomials. Applications to (twisted) jet differentials on projective spaces. https://arxiv.org/abs/2302.02634

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