Paris, 0507 October 2015
The tropicalization of an algebraic variety X over a
field k included in a ndimensional torus
is a piecewise linear variety which (roughly
speaking) is associated with the geometry of the
exponents appearing in the defining equations of X
and the relative sizes of the coefficients,
as measured with a valuation of k. Tropical
geometry provides us with tools that detect the
geometry of X from its tropicalization. But when
one changes the embeddings (or the variables)
the geometry of the equation changes and hence its
tropicalization does too. To deal with this,
one can construct a universal object which contains
all the tropicalizations (with all choices
of variables, embeddings), or can search for a
special embedding in order to have a tropical
variety which reflects the best the geometry
of X.
One goal of our meeting is to compare these two approaches.
On the other hand, Tropicalization can be thought as the inverse
manipulation to the construction
of toric varieties, in which we construct algebraic varieties from
combinatorial objects.
Tvarieties are generalizations of toric varieties.
Our
second goal is to meet these relatively new objects, whose construction
is not completely
combinatorial, and maybe to figure out what the inverse manipulation is.
Speakers :
Kevin Langlois (Bonn)
Hannah Markwig (Saarbrücken)
Bernard Teissier (Paris)
Organizers :
Hussein Mourtada, Matteo Ruggiero, Bernard Teissier.
