Related papers: On automorphisms of affine superspaces

For a smooth quasi-affine variety $X$, the affine closure $\overline{T^*X} := \text{Spec}(\mathbb{K}[T^*X])$ contains $T^*X$ as an open subset, and its smooth locus carries a symplectic structure. A natural question is whether…

We study the interaction between the group law on an abelian variety and the additive structure induced on its image under a morphism to projective space. Let $A/F$ be a simple abelian variety, $f:A \rightarrow \mathbb{P}^n$ be a morphism…

Let X be an irreducible smooth projective curve, of genus at least two, defined over an algebraically closed field of characteristic different from two. If X admits a nontrivial automorphism \sigma that fixes pointwise all the order two…

Let $F:\mathbb{C}[x_1,\ldots,x_n] \to \mathbb{C}[x_1,\ldots,x_n]$ be a $\mathbb{C}$-algebra endomorphism that has an invertible Jacobian. We bring two ideas concerning the Jacobian Conjecture: First, we conjecture that for all $n$, the…

The paper gives a complete description of local automorphism groups for Levi degenerate hypersurfaces of finite type in $\mathbb{C}^2$. We also prove that, with the exception of hypersurfaces of the form $v = |z|^k$, local automorphisms are…

We study parabolic automorphisms of irreducible holomorphically symplectic manifolds with a lagrangian fibration. Such automorphisms are (possibly up to taking a power) fiberwise translations on smooth fibers, and their orbits in a general…

We apply the coset character identities (generalization of Jacobi's abstruse identity) to compact and noncompact Gepner models. In the both cases, we prove that the partition function actually vanishes due to the spacetime supersymmetry. In…

A closed affine manifold is a closed manifold with coordinate patches into affine space whose transition maps are restrictions of affine automorphisms. Such a structure gives rise to a local diffeomorphism from the universal cover of the…

We show that every Lie algebra automorphisms of the vector fields $Vec(A^n)$ of affine n-space $A^n$, of the vector fields $Vec^c(A^n)$ with constant divergence, and of the vector fields $Vec^0(A^n)$ with divergence zero is induced by an…

Let $A$ be an abelian variety defined over $\bar{\mathbb{Q}}$, and let $\varphi$ be a dominant endomorphism of $A$ as an algebraic variety. We prove that either there exists a non-constant rational fibration preserved by $\varphi$, or there…

If F is an automorphism of the spectral unit ball, we show that, in a neighborhood of any cyclic (i.e. non-derogatory) matrix of the ball, the map F can be written as conjugation by a holomorphically varying non singular matrix. This…

In this paper, we first show that the Jacobian Conjecture is true for non-homogeneous power linear mappings under some conditions. Secondly, we prove an equivalent statement about the Jacobian Conjecture in dimension $r\geq 1$ and give some…

Let $A$ and $B$ be associative algebras over a field $F$ with {\rm char}$(F)\ne 2$. Our first main result states that if $A$ is unital and equal to its commutator ideal, then every Jordan epimorphism $\varphi:A\to B$ is the sum of a…

We prove an unexpected general relation between the Jacobian syzygies of a projective hypersurface $V\subset \mathbb{P}^n$ with only isolated singularities and the nature of its singularities. This allows to establish a new method for the…

Let $M$ be a product of rank-one symmetric spaces of compact type, each of dimension at least $3$. We establish sharp $L^p$ bounds for the restriction of Laplace--Beltrami eigenfunctions on $M$ to arbitrary submanifolds contained in a…

We show that Sarnak's conjecture on M\"obius disjointness holds in every uniquely ergodic modelof a quasi-discrete spectrum automorphism. A consequence of this result is that, for each non constant polynomial $P\in\R[x]$ with irrational…

Aim of this article is a Satake type theorem for super automorphic forms on a complex bounded symmetric super domain B of rank 1 with respect to a lattice. This theorem - roughly speaking - says that for large weight k and all p from 1 to…

For any algebraically closed field $K$ and any endomorphism $f$ of $\mathbb{P}^1(K)$ of degree at least 2, the automorphisms of $f$ are the M\"obius transformations that commute with $f$, and these form a finite subgroup of…

In this paper, we address the following two general problems: given two algebraic varieties in ${\bf C}^n$, find out whether or not they are (1) isomorphic; (2) equivalent under an automorphism of ${\bf C}^n$. Although a complete solution…

Let $X$ be a finite connected poset, $F$ a field and $I(X,F)$ the incidence algebra of $X$ over $F$. We describe the bijective linear idempotent preservers $\varphi:I(X,F)\to I(X,F)$. Namely, we prove that, whenever $\mathrm{char}(F)\ne 2$,…