Tropicalization of Varieties

Specialeforsvar ved Søren Frølich

Titel: Tropicalization of Varieties

Resume: Consider a field K equipped with a valuation map. We work over the tropical algebra which is a semi ring where addition is minimum and multiplication is addition. This turns every polynomial into a piece-wise linear map. We begin by defining tropical hypersurfaces from a tropical polynomial F to be the points where F is not linear. We will show that this is the same as taking the closure of the coordinate wise valuation. Then we will generalize this to subvarieties of a torus T and then to arbitrary toric varieties. We will end with a discussion of how to tropicalize a variety embedded in the affine space.

Vejleder: Lars H. Halle
censor: Peter Beelen, DTU