Woensdag 4 oktober 2006
Vanaf kwart voor 11 is er koffie en thee in de
||Michiel de Bondt (RU)
||Herbie, a Druzkowski counterexample to the linear dependence problem
||11:00 - 12:00
(voor de zaal).
In 1992 several people independently made the following conjecture,
now known as:
Let H := (H1, ..., Hn)
be a homogeneous polynomial
map from Cn
to itself of degree 3
(i.e. each Hi
is homogeneous of degree 3 or zero)
such that the Jacobian matrix JH
Are the rows of JH
linearly dependent over C
The importance of this question comes from the fact that it is related
to the Jacobian Conjecture. In 2005 the speaker found the first
counterexample in dimension 10 (and won a bottle of Polish Vodka,
offered since 1993, for his solution).
However, the question remained if a similar counterexample exists for a
so-called Druzkowski mapping, i.e. a mapping as above such that each
Hi is a third power of a linear form.
In this talk the solution to the problem will be discussed:
a counterexample in dimension 53.