Lifting tropical curves in space and linear systems on graphs

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• 作者：Eric Katz ^{eekatz@math.uwaterloo.ca}
• 关键词：Tropical geometry ; Linear systems on graphs ; Deformation theory
• 刊名：Advances in Mathematics
• 出版年：2012
• 期刊代码：62_00018708
• 类别：mt
• 出版时间：20 June, 2012
• 卷：230
• 期：3
• 页码：853-875
• 文件大小：297 K

摘要

Tropicalization is a procedure for associating a polyhedral complex in Euclidean space to a subvariety of an algebraic torus. We study the question of which graphs arise from tropicalizing algebraic curves. By using Baker鈥檚 specialization of linear systems from curves to graphs, we are able to give a necessary condition for a balanced weighted graph to be the tropicalization of a curve. Our condition reproduces a generalization of Speyer鈥檚 well-spacedness condition and also gives new conditions. In addition, it suggests a new combinatorial structure on tropicalizations of algebraic curves.