Special Lectures in Real & Complex Geometry

Thursday, 5.3.2009, 16:00-17:00, place: Schreiber 309

Note special day and time!


Thomas Markwig, Kaiserslautern University

The tropical j-invariant


Abstract
             
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.