Abstracts for the Seminar
 Discrete Geometry and Combinatorics
 Spring 2017

Speaker:  Yoav Len, University of Waterloo
Title: Curves, graphs, and tangent lines
Time: 2:30 PM, Monday, April 17, 2017
Place:  Malott 206

Abstract: I will discuss the interplay between tangent lines of algebraic and tropical curves. By tropicalizing all the tangent lines of a plane curve, we obtain the tropical dual curve, and a recipe for computing the Newton polygon of the dual projective curve. In the case of canonical curves, tangent lines are closely related with various phenomena in algebraic geometry such as double covers, theta characteristics and Prym varieties. When degenerating them in families, we discover analogous constructions in tropical geometry, and links between quadratic forms, covers of graphs and tropical bi-tangents.

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