Second main theorem in the tropical projective space

作者：Korhonen Risto^*; Tohge Kazuya

来源：Advances in Mathematics, 2016, 298: 693-725.

DOI：10.1016/j.aim.2016.05.003

• Tropical Nevanlinna theory
• Cartan characteristic
• Tropical projective space

Tropical Nevanlinna theory, introduced by Halburd and Southall as a tool to analyze integrability of ultra-discrete equations, studies the growth and complexity of continuous piecewise linear real functions. The purpose of this paper is to extend tropical Nevanlinna theory to n-dimensional tropical projective spaces by introducing a natural characteristic function for tropical holomorphic curves, and by proving a tropical analogue of Cartan's second main theorem. It is also shown that in the 1-dimensional case this result implies a known tropical second main theorem due to Laine and Tohge.

• 出版日期2016-8-6