Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On multidegree of tame and wild automorphisms of C^3   In this note we show that the set mdeg(Aut(C^3)) mdeg(Tame(C^3)) is not
empty. Moreover we show that this set has infinitely many elements. Since for
the famous Nagata's example N of wild automorphism, mdeg N =(5,3,1) is an
element of mdeg(Tame(C^3)) and since for other known examples of wild
automorphisms the multidegree is of the form (1,d_2,d_3) (after permutation if
neccesary), then we give the very first exmple of wild automorphism F of C^3
such that mdeg F does not belong to mdeg(Tame(C^3)).
  We also show that, if d_1,d_2 are odd numbers such that gcd (d_1,d_2) =1,
then (d_1,d_2,d_3) belongs to mdeg(Tame(C^3)) if and only if d_3 is a linear
combination of d_1,d_2 with natural coefficients. This a crucial fact that we
use in the proof of the main result.

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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol