6 problems

Zaitsev's conjecture. 1-jets suffice to determine all local automorphisms of $M$, except when $M$ is biholomorphic to the sphere at a generic point, which is the case of $S_k$.

Let $M\subset \mathbb C^N$ be a connected holomorphically nondegenerate real-analytic generic submanifold of finite type at some point. For every $p\in M$, let ${\rm Aut}(M,p)$ be…

Let $M\subset\mathbb C^{n+d}$ be a strongly Levi nondegenerate model quadric, let $a\in\mathbb C^d$ be sufficiently small, and let $V\in\mathbb C^n$ be as in the definition of…

Let $M\subset\mathbb C^{n+d}$ be a strongly Levi nondegenerate real submanifold through $0$, and let $a\in\mathbb C^d$ be sufficiently small. Suppose that $M$ is $\mathfrak{D}(a)$-…

Beloshapka–Ezhov–Meylan conjecture. Under these hypotheses, the $1$-jet map $\mathfrak j_{1}$ should be a local diffeomorphism.

2-jet determination conjecture. Under these hypotheses, any germ at $p$ of a CR automorphism of $M$ of class $\mathcal{C}^3$ is uniquely determined by its $2$-jet at $p$.