266,187 research outputs found
Normal origamis of Mumford curves
An origami (also known as square-tiled surface) is a Riemann surface covering
a torus with at most one branch point. Lifting two generators of the
fundamental group of the punctured torus decomposes the surface into finitely
many unit squares. By varying the complex structure of the torus one obtains
easily accessible examples of Teichm\"uller curves in the moduli space of
Riemann surfaces. The p-adic analogues of Riemann surfaces are Mumford curves.
A p-adic origami is defined as a covering of Mumford curves with at most one
branch point, where the bottom curve has genus one. A classification of all
normal non-trivial p-adic origamis is presented and used to calculate some
invariants. These can be used to describe p-adic origamis in terms of glueing
squares.Comment: 21 pages, to appear in manuscripta mathematica (Springer
Hyperelliptic Integrable Systems on K3 and Rational Surfaces
We show several examples of integrable systems related to special K3 and
rational surfaces (e.g., an elliptic K3 surface, a K3 surface given by a double
covering of the projective plane, a rational elliptic surface, etc.). The
construction, based on Beauvilles's general idea, is considerably simplified by
the fact that all examples are described by hyperelliptic curves and Jacobians.
This also enables to compare these integrable systems with more classical
integrable systems, such as the Neumann system and the periodic Toda chain,
which are also associated with rational surfaces. A delicate difference between
the cases of K3 and of rational surfaces is pointed out therein.Comment: LaTeX2e using packages "amsmath,amssymb", 15 pages, no figur
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