| It
turns out that many interesting properties of algebraic varieties are
preserved under the process of tropicalisation. We will explain
during this talk what tropicalisation is, and we will give one
example for the above statement. To be more precise, if we start on the
algebraic side with a smooth elliptic curve, i.e. a curve of genus one,
then under good circumstances the tropicalisation will be a piecewise
linear with precisely one loop, i.e. the graph will have genus one. It
turns out that the length of this loop is related to the j-invariant of
the elliptic curve. |