67,430 research outputs found
Real algebraic surfaces with isolated singularities
Given a real algebraic surface S in RP3, we propose a constructive procedure to determine the topology of S and to compute non-trivial topological invariants for the pair (RP3, S) under the hypothesis that the real singularities of S are isolated. In particular, starting from an implicit equation of the surface, we compute the number of connected components of S, their Euler characteristics and the weighted 2-adjacency graph of the surface
Affine algebraic groups with periodic components
A connected component of an affine algebraic group is called periodic if all
its elements have finite order. We give a characterization of periodic
components in terms of automorphisms with finite number of fixed points. It is
also discussed which connected groups have finite extensions with periodic
components. The results are applied to the study of the normalizer of a maximal
torus in a simple algebraic group.Comment: 20 page
A connectedness property of algebraic moment maps
Let a connected reductive group G act on the smooth connected variety X. The
cotangent bundle of X is a Hamiltonian G-variety. We show that its "total
moment map" has connected fibers.
This is an expanded version of section 6 of my paper dg-ga/9712010 on Weyl
groups of Hamiltonian manifolds.Comment: 15 page
AdS4 backgrounds with N>16 supersymmetries in 10 and 11 dimensions
We explore all warped backgrounds with the most
general allowed fluxes that preserve more than 16 supersymmetries in -
and -dimensional supergravities. After imposing the assumption that either
the internal space is compact without boundary or the isometry
algebra of the background decomposes into that of AdS and that of
, we find that there are no such backgrounds in IIB supergravity.
Similarly in IIA supergravity, there is a unique such background with 24
supersymmetries locally isometric to , and in
supergravity all such backgrounds are locally isometric to the maximally
supersymmetric solution.Comment: 53 pages. v2: minor changes and references added. v3: typos corrected
and minor footnote added, published versio
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