16,213 research outputs found
On superheight conditions for the affineness of open subsets
In this paper we consider the open complement U of a hypersurface Y=V(a) in
an affine scheme X. We study the relations between the affineness of U, the
intersection of Y with closed subschemes, the property that every closed
surface in U is affine, the property that every analytic closed surface is
Stein and the superheight of the defining ideal a.Comment: 20 page
Weight functions on non-archimedean analytic spaces and the Kontsevich-Soibelman skeleton
We associate a weight function to pairs consisting of a smooth and proper
variety X over a complete discretely valued field and a differential form on X
of maximal degree. This weight function is a real-valued function on the
non-archimedean analytification of X. It is piecewise affine on the skeleton of
any regular model with strict normal crossings of X, and strictly ascending as
one moves away from the skeleton. We apply these properties to the study of the
Kontsevich-Soibelman skeleton of such a pair, and we prove that this skeleton
is connected when X has geometric genus one. This result can be viewed as an
analog of the Shokurov-Kollar connectedness theorem in birational geometry.Comment: Latex, 39 pages. Changes w.r.t. v2: construction of the weight
function and the skeleton extended to pluricanonical form
Relative Orbifold Donaldson-Thomas Theory and the Degeneration Formula
We generalize the notion of expanded degenerations and pairs for a simple
degeneration or smooth pair to the case of smooth Deligne-Mumford stacks. We
then define stable quotients on the classifying stacks of expanded
degenerations and pairs and prove the properness of their moduli's. On
3-dimensional smooth projective DM stacks this leads to a definition of
relative Donaldson-Thomas invariants and the associated degeneration formula.Comment: 59 pages. Final versio
- …