64 research outputs found
Moduli spaces of d-connections and difference Painleve equations
We show that difference Painleve equations can be interpreted as isomorphisms
of moduli spaces of d-connections on the projective line with given singularity
structure. We also derive a new difference equation. It is the most general
difference Painleve equation known so far, and it degenerates to both
difference Painleve V and classical (differential) Painleve VI equations.Comment: 30 pages (LaTeX
An example of the Langlands correspondence for irregular rank two connections on P^1
Special kinds of rank 2 vector bundles with (possibly irregular) connections
on P^1 are considered. We construct an equivalence between the derived category
of quasi-coherent sheaves on the moduli stack of such bundles and the derived
category of modules over a TDO ring on certain non-separated curve. We identify
this curve with the coarse moduli space of some parabolic bundles on P^1. Then
our equivalence becomes an example of the categorical Langlands correspondence.Comment: Section 5 was shortened by referring to results of Hernandez Ruiperez
et al. The reader might want to look at the previous (2nd) version for a more
self-contained exposition. Other minor change
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