Geometry of Tropical Varieties with Applications - Lecture 3

Explore the intricacies of tropical geometry in this third lecture on the geometry of tropical varieties and their applications. Delve into key concepts such as fans, fanfolds, tropical fans, and tropical fanfolds, with illustrative examples provided. Learn about operations and constructions on tropical fans and fanfolds, including products and star subdivisions. Examine divisors on tropical fans, their construction, and the concept of principal divisors. Investigate tropical modifications and their properties through propositions. Discover the importance of shellability for tropical fans and fanfolds, supported by examples and theorems. Engage with the material through a Q&A session at the end of this comprehensive 1-hour 9-minute lecture presented by Omid Amini at the International Centre for Theoretical Sciences.

Geometry of tropical varieties with a view toward applications Lecture 3
Summary
Fan
Fanfold
Tropical fan
Tropical fanfold
Example
6. Geometry of tropical fanfolds
Operations and constructions on tropical fans and fanfolds
Product
Star subdivision
Divisiors on tropical fans
Construction
Definition Principal divisor
Tropical modification
Proposition
Shellability for tropical fans and tropical fanfolds
Examples
Theorem A-Piquerez
Q&A
Wrap Up