Repairing tropical curves by means of tropical modifications

Series: 
Algebra Seminar
Monday, October 26, 2015 - 15:05
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
The Ohio State University
Organizer: 
Tropical geometry is sensitive to embeddings of algebraic varieties inside toric varieties. In this talk, I will advertise tropical modifications as a tool to locally repair bad embeddings of plane curves, allowing the re-embedded tropical curve to better reflect the geometry of the input one.  Our motivating examples will be plane elliptic cubics and genus two hyperelliptic curves.  Based on joint work with Hannah Markwig (arXiv:1409.7430) and ongoing work in progress with Hannah Markwig and Ralph Morrison.