77 research outputs found
On total reality of meromorphic functions
We show that if a meromorphic function of degree at most four on a real
algebraic curve of an arbitrary genus has only real critical points then it is
conjugate to a real meromorphic function after a suitable projective
automorphism of the image.Comment: 13 page
A Non-Algebraic Patchwork
Itenberg and Shustin's pseudoholomorphic curve patchworking is in principle
more flexible than Viro's original algebraic one. It was natural to wonder if
the former method allows one to construct non-algebraic objects. In this paper
we construct the first examples of patchworked real pseudoholomorphic curves in
whose position with respect to the pencil of lines cannot be
realised by any homologous real algebraic curve.Comment: 6 pages, 1 figur
Two dimensional periodic box-ball system and its fundamental cycle
We study a 2-dimensional Box-Ball system which is a ultradiscrete analog of
the discrete KP equation. We construct an algorithm to calculate the
fundamental cycle, which is an important conserved quantity of the 2-dim.
Box-Ball system with periodic boundary condition, by using the tropical curve
theory.Comment: 16 pages, 5 figure
- …