For related talk material Taida Institute for Mathematical Sciences(TIMS)


TIMS Taipei Number Theory Seminar (2017 Fall)

Analytification of an affine curve as the limit of tropicalizations of bounded degree

Prof. Shu Kawaguchi

2017 - 09 - 15 (Fri.)
13:00 - 15:00
103, Mathematics Research Center Building (ori. New Math. Bldg.)

Let K be an algebraically closed field that is complete with respect to a nontrivial nonarchimedean valuation. In the paper ``Analytification is the limit of all tropicalizations,'' Payne showed among other things that if X is an affine variety over K, then tropicalizations of various embeddings of X into affine space give rise to analytification of X in the sense of Berkovich. In this talk, we explain that if X is an affine curve in A^N with smooth compactification in P^N, then embeddings of X of bounded degree give rise to analytification of X. For example, analytification of an affine plane curve of genus 1 is the limit of linear tropicalizations (as shown in Baker, Rabinoff and Payne), and analytification of an affine plane curve of genus 3 is the limit of quadratic tropicalizations. This is joint work with Kazuhiko Yamaki.