Computing Severi Degrees with Long-edge Graphs

Abstract

We study a class of graphs with finitely many edges in order to understand the nature of the formal logarithm of the generating series for Severi degrees in elementary combinatorial terms. These graphs are related to floor diagrams associated to plane tropical curves originally developed by Brugalle and Mikhalkin, and used by Block, Fomin, and Mikhalkin to calculate Severi degrees of the projective plane and node polynomials of plane curves.

Minor changes, including revised references, and an observation due to S. Chmutov about a relation with chromatic polynomials. 20 pages, 16 figures. To appear in a volume of the Bulletin of the Brazilian Math Society devoted to proceedings of 2012 ALGA at IMPA