Ph.D in Mathematics

 

PHD MINICOURSE:
TITLE: Scheme theoretic tropicalization
SPEAKER: Olivier Lorscheid (IMPA, Rio de Janeiro)
TIMETABLE: Monday 22 February, hour 11-13 (Room 311) Tuesday 23 Feb

22/02/2016 - 11:00
Room 311 - third floor - Math Department of the University of Roma Tre

ABSTRACT: After Kajiwara and Payne's works in the late 2000's, it was well-understood how to tropicalize a closed subvariety of a toric variety. In recent years, this process got generalized in different direcetions. While Jeff and Noah Giansiracusa enhanced tropical varieties with an underlying scheme structure, employing the theory of so-called semiring schemes, Thuillier and Ulirsch replaced the ambient toric variety by toroidal embeddings, or more general, a log structure. In this series of three lectures, we will show how all of these theories can be understood on a common basis by using the language of so-called blueprints. After reviewing the above mentioned concepts, we will introduce bluprints and blue schemes. We redefine the tropicalization of a variety as the solution to a certain moduli problem and consruct the corresponding moduli space under some ambient hypothesis. Finally, we show how to recover the above mentioned theories within the languange of blue schemes.