
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, 381 Komaba, Meguro, Tokyo, 1538914, Japan
Received September 02, 2015, in final form June 17, 2016; Published online June 24, 2016
Abstract
Let $\{V_q\}_{q}$ be a complex oneparameter 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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