221,963 research outputs found
In search of an appropriate abstraction level for motif annotations
In: Proceedings of the 2012 Workshop on Computational Models of Narrative, (pp. 22-28).
Metric uniformization of morphisms of Berkovich curves
We show that the metric structure of morphisms between
quasi-smooth compact Berkovich curves over an algebraically closed field admits
a finite combinatorial description. In particular, for a large enough skeleton
of , the sets of points of of
multiplicity at least in the fiber are radial around with the
radius changing piecewise monomially along . In this case, for any
interval connecting a rigid point to the skeleton, the
restriction gives rise to a piecewise monomial function
that depends only on the type 2 point
. In particular, the metric structure of is determined by
and the family of the profile functions with
. We prove that this family is piecewise monomial in
and naturally extends to the whole . In addition, we extend
the theory of higher ramification groups to arbitrary real-valued fields and
show that coincides with the Herbrand's function of
. This gives a curious geometric
interpretation of the Herbrand's function, which applies also to non-normal and
even inseparable extensions.Comment: second version, 28 page
Morse Inequalities for Orbifold Cohomology
This paper begins the study of Morse theory for orbifolds, or more precisely
for differentiable Deligne-Mumford stacks. The main result is an analogue of
the Morse inequalities that relates the orbifold Betti numbers of an
almost-complex orbifold to the critical points of a Morse function on the
orbifold. We also show that a generic function on an orbifold is Morse. In
obtaining these results we develop for differentiable Deligne-Mumford stacks
those tools of differential geometry and topology -- flows of vector fields,
the strong topology -- that are essential to the development of Morse theory on
manifolds
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