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تسجيل مستخدم جديدQuadratic homogeneous polynomial maps $H$ and Keller maps $x+H$ with $rk JH=3$
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We classify all quadratic homogeneous polynomial maps $H$ and Keller maps of the form $x + H$, for which $rk J H = 3$, over a field $K$ of arbitrary characteristic. In particular, we show that such a Keller map (up to a square part if $char K=2$) is a tame automorphism.
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We compute by hand all quadratic homogeneous polynomial maps $H$ and all Keller maps of the form $x + H$, for which ${rm rk} J H = 3$, over a field of arbitrary characteristic. Furthermore, we use computer support to compute Keller maps of the form
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We classify Keller maps $x + H$ in dimension $n$ over fields with $tfrac16$, for which $H$ is homogeneous, and (1) deg $H = 3$ and rk $JH le 2$; (2) deg $H = 3$ and $n le 4$; (3) deg $H = 4$ and $n le 3$; (4) deg $H = 4 = n$ and $H_1, H_2, H_
3, H_4$ are linearly dependent over $K$. In our proof of these classifications, we formulate (and prove) several results which are more general than needed for these classifications. One of these results is the classification of all homogeneous polynomial maps $H$ as in (1) over fields with $tfrac16$.
Let $K$ be any field with $textup{char}K eq 2,3$. We classify all cubic homogeneous polynomial maps $H$ over $K$ with $textup{rk} JHleq 2$. In particular, we show that, for such an $H$, if $F=x+H$ is a Keller map then $F$ is invertible, and furthermore $F$ is tame if the dimension $n eq 4$.
Let $K$ be any field and $x = (x_1,x_2,ldots,x_n)$. We classify all matrices $M in {rm Mat}_{m,n}(K[x])$ whose entries are polynomials of degree at most 1, for which ${rm rk} M le 2$. As a special case, we describe all such matrices $M$, which are th
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Motivated by the dynamical uniform boundedness conjecture of Morton and Silverman, specifically in the case of quadratic polynomials, we give a formal construction of a certain class of dynamical analogues of classical modular curves. The preperiodic
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