1,883 research outputs found
Topological noetherianity for cubic polynomials
Let be the space of complex cubic polynomials in
infinitely many variables. We show that this space is
-noetherian, meaning that any
-stable Zariski closed subset is cut out by finitely many
orbits of equations. Our method relies on a careful analysis of an invariant of
cubics introduced here called q-rank. This result is motivated by recent work
in representation stability, especially the theory of twisted commutative
algebras. It is also connected to certain stability problems in commutative
algebra, such as Stillman's conjecture.Comment: 13 page
Multiple concentric annuli for characterizing spatially nonuniform backgrounds
A method is presented for estimating the background at a given location on a
sky map by interpolating the estimated background from a set of concentric
annuli which surround this location. If the background is nonuniform but
smoothly varying, this method provides a more accurate (though less precise)
estimate than can be obtained with a single annulus. Several applications of
multi-annulus background estimation are discussed, including direct testing for
point sources in the presence of a nonuniform background, the generation of
"surrogate maps" for characterizing false alarm rates, and precise testing of
the null hypothesis that the background is uniform.Comment: 35 pages, including 19 embedded postscript figures; LaTeX with AAS
macros. Minor revisions, improved figures, as suggested by referee. To appear
in Astrophysical Journa
Tachyon Condensation on the Elliptic Curve
We use the framework of matrix factorizations to study topological B-type
D-branes on the cubic curve. Specifically, we elucidate how the brane RR
charges are encoded in the matrix factors, by analyzing their structure in
terms of sections of vector bundles in conjunction with equivariant R-symmetry.
One particular advantage of matrix factorizations is that explicit moduli
dependence is built in, thus giving us full control over the open-string moduli
space. It allows one to study phenomena like discontinuous jumps of the
cohomology over the moduli space, as well as formation of bound states at
threshold. One interesting aspect is that certain gauge symmetries inherent to
the matrix formulation lead to a non-trivial global structure of the moduli
space. We also investigate topological tachyon condensation, which enables us
to construct, in a systematic fashion, higher-dimensional matrix factorizations
out of smaller ones; this amounts to obtaining branes with higher RR charges as
composites of ones with minimal charges. As an application, we explicitly
construct all rank-two matrix factorizations.Comment: 69p, 6 figs, harvmac; v2: minor change
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