### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 061, 23 pages      arXiv:1509.00175      https://doi.org/10.3842/SIGMA.2016.061

### Geometric Monodromy around the Tropical Limit

Yuto Yamamoto
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, 153-8914, Japan

Received September 02, 2015, in final form June 17, 2016; Published online June 24, 2016

Abstract
Let $\{V_q\}_{q}$ be a complex one-parameter family of smooth hypersurfaces in a toric variety. In this paper, we give a concrete description of the monodromy transformation of $\{V_q\}_q$ around $q=\infty$ in terms of tropical geometry. The main tool is the tropical localization introduced by Mikhalkin.

Key words: tropical geometry; monodromy.

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