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Results tagged with arakelov-theory
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user 26522
13
votes
Smoothness of the "Archimedean special fiber" in Arakelov geometry
In Arakelov geometry, the conventional wisdom is that the ``closed fibre at $\infty$'' should be viewed as totally degenerate. This is the extreme opposite of smoothness. A visualization in the case o …
- 13.8k
8
votes
0
answers
502
views
Points of minimum Arakelov height and harmonic arithmetical varieties
Added. (28/2) To put it less pompously (and more vaguely, less concretely), I wanted to relate the impression that it is the general rule that an Arakelov (i.e., geometric) height on an arithmetical v …
3
votes
1
answer
276
views
Mumford-Ramanujam examples in characteristic p [and in Arakelov geometry]
For a compact Riemann surface $B$ of genus $\geq 2$, it is a consequence of the Narasimhan-Seshadri theorem that there exist rank-$2$ vector bundles $E \to B$ of degree zero, all of whose symmetric po …
- 13.8k