Xiaosong Sun

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20182025

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math.AG2025

Dynamical degrees of affine-triangular automorphisms in dimension four

Enbo Shao, Xiaosong Sun

In this paper, let k be the affine n-space over an arbitrary field k. We show that dynamical degrees of affine-triangular automorphisms in dimension 4 are algebraic integers of deg…

math.AG2018

Quadratic homogeneous polynomial maps $H$ and Keller maps $x + H$ with $r k J H = 3$

Michiel de Bondt, Xiaosong Sun

We classify all quadratic homogeneous polynomial maps $H$ and Keller maps of the form $x + H$ , for which $r k J H = 3$ , over a field $K$ of arbitrary characteristic. In particular,…

math.AG2018

Classification of cubic homogeneous polynomial maps with Jacobian matrices of rank two

Michiel de Bondt, Xiaosong Sun

Let $K$ be any field with $char K \neq = 2, 3$ . We classify all cubic homogeneous polynomial maps $H$ over $K$ with $rk J H \leq 2$ . In particular, we show that, for suc…

math.AG2018

A case of the generalized vanishing conjecture

Zhenzhen Feng, Xiaosong Sun

In this paper, we show that the GVC (generalized vanishing conjecture) holds for the differential operator $Λ = (\partial_{x} - Φ (\partial_{y})) \partial_{y}$ and all polynomials $P (x, y)$ , wh…

Dynamical degrees of affine-triangular automorphisms in dimension four

Quadratic homogeneous polynomial maps H and Keller maps x+H with rkJH=3

Classification of cubic homogeneous polynomial maps with Jacobian matrices of rank two

A case of the generalized vanishing conjecture

Quadratic homogeneous polynomial maps $H$ and Keller maps $x + H$ with $r k J H = 3$