Geodesic
Nonaffine differential-algebraic curves do not exist
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2017), pp. 3-8 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper outlines why the spectrum of maximal ideals ${\rm Spec}_\mathbb{C} A$ of a countably-dimensional differential $\mathbb{C}$-algebra $A$ of transcendence degree 1 without zero devisors is locally analytic, which means that for any $\mathbb{C}$-homomorphism $\psi_M : A \to \mathbb{C}$ ($M \in {\rm Spec}_{\mathbb{C}} A$) and any $a \in A$ the Taylor series $\widetilde{\psi}_M (a) \stackrel{{\rm def}}{=} \sum\limits_{m=0}^{\infty} \psi_M(a^{(m)}) \frac{z^m}{m!}$ has nonzero radius of convergence depending on the element $a \in A$. 
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     author = {O. V. Gerasimova and Yu. P. Razmyslov},
     title = {Nonaffine differential-algebraic curves do not exist},
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O. V. Gerasimova; Yu. P. Razmyslov. Nonaffine differential-algebraic curves do not exist. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2017), pp. 3-8. http://geodesic.mathdoc.fr/item/VMUMM_2017_3_a0/

[1] Shafarevich I.R., Osnovy algebraicheskoi geometrii, MTsNMO, M., 2007 | MR

[2] Gerasimova O.V., Pogudin G.A., Razmyslov Yu.P., “Rolling simplexes and their commensurability, III (Sootnosheniya Kapelli i ikh primeneniya v differentsialnykh algebrakh)”, Fund. i prikl. matem., 19:6 (2014), 7–24 | MR