In
tropical geometry, algebraic curves are replaced by piece-wise
linear degenerations called tropical curves. Even though we "lose a lot
of information" with this degeneration, many properties of the
algebraic curve can be read off the tropical curve, and many theorems
that hold for algebraic curves can be shown on the tropical side. One
of the fields in which tropical geometry has had a lot of
successrecently is enumerative geometry. In this talk, we present an
enumerativeinvariant - namely the number of plane elliptic curves of a
given degree d with fixed j-invariant through 3d-1 points in general
position - that can be read off the tropical side. We present a
tropical way to determine these numbers. This talk follows a talk given
by Thomas Markwig who shows how the j-invariant of a curve is
reflected in the tropical world. Joint work with Michael Kerber.
|
