292 research outputs found
Variants of normality for Noetherian schemes
This note presents a uniform treatment of normality and three of its
variants---topological, weak and seminormality---for Noetherian schemes. The
key is to define these notions for pairs consisting of a (not
necessarily reduced) scheme and a closed, nowhere dense subscheme . An
advantage of the new definitions is that, unlike the usual absolute ones, they
are preserved by completions. This shortens some of the proofs and leads to
more general results. Version 2: small changes
Circle actions on simply connected 5--manifolds
The aim of this paper is to study compact 5--manifolds which admit fixed
point free circle actions. The first result implies that the torsion in the
second homology and the second Stiefel--Whitney class have to satisfy strong
restrictions. We then show that for simply connected 5--manifolds these
restrictions are necessary and sufficient
Simultaneous normalization and algebra husks
The aim of this note is to use the concept of algebra husks to prove an
analog of the flattening decomposition theorem for simultaneous normalizations.
Other applications improve earlier flatness criteria. Parts of this note were
contained in the first version of "Hulls and Husks" (arXiv:0805.0576).
Dec. 16: new references added
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