The genus formula and tropical geometry
|Speaker:||Professor Eric Katz|
|Affiliation:||University of Waterloo|
|Room:||Mathematics and Computer Building (MC) 4040|
A complex homogeneous polynomial in three variables describes an algebraic curve in projective space. This algebraic curve is a topologically a surface. We can ask what is the genus of the surface is in terms of the degree of the polynomial. This is the celebrated genus formula. We will prove it by decomposing the surface into simpler surfaces called pairs-of-pants. In doing so, we will introduce techniques of tropical geometry.
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