Mathematics – Algebraic Geometry
Scientific paper
2009-11-29
J. Pure Appl. Algebra 215 (2011), no. 12, 2843-2846
Mathematics
Algebraic Geometry
Scientific paper
10.1016/j.jpaa.2011.04.003
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.
Karaś Marek
Zygadlo Jakub
No associations
LandOfFree
On multidegree of tame and wild automorphisms of C^3 does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On multidegree of tame and wild automorphisms of C^3, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On multidegree of tame and wild automorphisms of C^3 will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-150880