27,849 research outputs found
Geometricity of the Hodge filtration on the -stack of perfect complexes over
We construct a locally geometric -stack of perfect
complexes with -connection structure on a smooth projective variety
. This maps to , so it can be considered as the Hodge filtration
of its fiber over 1 which is , parametrizing complexes of
-modules which are -perfect. We apply the result of Toen-Vaquie that
is locally geometric. The proof of geometricity of the map
uses a Hochschild-like notion of weak complexes
of modules over a sheaf of rings of differential operators. We prove a
strictification result for these weak complexes, and also a strictification
result for complexes of sheaves of -modules over the big crystalline site
A weight two phenomenon for the moduli of rank one local systems on open varieties
The twistor space of representations on an open variety maps to a weight two
space of local monodromy transformations around a divisor component at infinty.
The space of -invariant sections of this slope-two bundle over the
twistor line is a real 3 dimensional space whose parameters correspond to the
complex residue of the Higgs field, and the real parabolic weight of a harmonic
bundle
Explaining Gabriel-Zisman localization to the computer
This explains a computer formulation of Gabriel-Zisman localization of
categories in the proof assistant Coq. It includes both the general
localization construction with the proof of GZ's Lemma 1.2, as well as the
construction using calculus of fractions. The proof files are bundled with the
other preprint "Files for GZ localization" posted simultaneously
Formalized proof, computation, and the construction problem in algebraic geometry
An informal discussion of how the construction problem in algebraic geometry
motivates the search for formal proof methods. Also includes a brief discussion
of my own progress up to now, which concerns the formalization of category
theory within a ZFC-like environment
Asymptotics for general connections at infinity
For a standard path of connections going to a generic point at infinity in
the moduli space of connections on a compact Riemann surface, we show
that the Laplace transform of the family of monodromy matrices has an analytic
continuation with locally finite branching. In particular the convex subset
representing the exponential growth rate of the monodromy is a polygon, whose
vertices are in a subset of points described explicitly in terms of the
spectral curve. Unfortunately we don't get any information about the size of
the singularities of the Laplace transform, which is why we can't get
asymptotic expansions for the monodromy.Comment: My talk at the Ramis conference, Toulouse, September 200
Fixed points and lines in 2-metric spaces
We consider bounded 2-metric spaces satisfying an additional axiom, and show
that a contractive mapping has either a fixed point or a fixed line.Comment: adds reference
Moduli as Inflatons in Heterotic M-theory
We consider different cosmological aspects of Heterotic M-theory. In
particular we look at the dynamical behaviour of the two relevant moduli in the
theory, namely the length of the eleventh segment (pi rho) and the volume of
the internal six manifold (V) in models where supersymmetry is broken by
multiple gaugino condensation. We look at different ways to stabilise these
moduli, namely racetrack scenarios with or without non-perturbative corrections
to the Kahler potential. The existence of different flat directions in the
scalar potential, and the way in which they can be partially lifted, is
discussed as well as their possible role in constructing a viable model of
inflation. Some other implications such as the status of the moduli problem
within these models are also studied.Comment: 16 pages, 8 Postscript figures. Final version to appear in JHE
Seminatural bundles of rank two, degree one and on a quintic surface
In this paper we continue our study of the moduli space of stable bundles of
rank two and degree 1 on a very general quintic surface. The goal in this paper
is to understand the irreducible components of the moduli space in the first
case in the "good" range, which is . We show that there is a single
irreducible component of bundles which have seminatural cohomology, and
conjecture that this is the only component for all stable bundles
On the classification of rank two representations of quasiprojective fundamental groups
Suppose is a smooth quasiprojective variety over \cc and \rho : \pi
_1(X,x) \to SL(2,\cc) is a Zariski-dense representation with quasiunipotent
monodromy at infinity. Then factors through a map with
either a DM-curve or a Shimura modular stack.Comment: minor changes in exposition, citation
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