Abstract:
The extended Catalan arrangement of type $B_2$ is defined as the coning of lines $x=k$, $y=k$, $x\pm y=k$ ($k=-m,\dots,m$).
Its logarithmic vector field is known to be free, but explicit shape of the basis was not known until recently.
I will give a short introduction on the (mulit-)arrangement theory and explain how to construct an explicit basis for the extended Catalan arrangement of type $B_2$.