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Seminar

Language	English
From	2013/07/05 10:30
To	2013/07/05 12:00
Place	Room 152, Building No.3, Faculty of Science, Kyoto University
Seminar Name	Algebra Geometrical Seminar
Title	The Schottky Problem in Genus Five
Field	Algebra Geometry
Speakers	Kazuhiko Yamaki
Affiliation	Kyoto University
Abstract	Let $(G, \omega)$ be a hyperelliptic vertex-weighted graph of genus $g \geq 2$ . We give a characterization of $(G, \omega)$ for which there exists a smooth projective curve $X$ of genus $g$ over a complete discrete valuation field with reduction graph $(G, \omega)$ such that the ranks of any divisors are preserved under specialization. We explain, for a given vertex-weighted graph $(G, \omega)$ in general, how the existence of such $X$ relates the Riemann--Roch formulae for $X$ and $(G, \omega)$ , and also how the existence of such $X$ is related to a conjecture of Caporaso. This is a joint work with S. Kawaguchi.
Link	http://www.math.kyoto-u.ac.jp/~abetaku/agseminar.htm