66,885 research outputs found
Permanence properties of -injectivity
We prove that -injectivity localizes, descends under faithfully flat
homomorphisms, and ascends under flat homomorphisms with Cohen-Macaulay and
geometrically -injective fibers, all for arbitrary Noetherian rings of prime
characteristic. As a consequence, we show that the -injective locus is open
on most rings arising in arithmetic and geometry. Furthermore, we prove that
over an algebraically closed field of positive characteristic, generic
projection hypersurfaces associated to normal projective varieties are weakly
normal, and generic projection hypersurfaces associated to suitably embedded
smooth projective varieties of low dimension are even -pure, and hence
-injective. The former result proves a conjecture of Bombieri and
Andreotti-Holm, and the latter result is the positive characteristic analogue
of a theorem of Doherty.Comment: 38 pages; comments welcome! v2: added Theorem 6.6, fixed Lemma A.2,
more transparent proof of Lemma 4.5, other small additions and change
High Angular Resolution Stellar Imaging with Occultations from the Cassini Spacecraft II: Kronocyclic Tomography
We present an advance in the use of Cassini observations of stellar
occultations by the rings of Saturn for stellar studies. Stewart et al. (2013)
demonstrated the potential use of such observations for measuring stellar
angular diameters. Here, we use these same observations, and tomographic
imaging reconstruction techniques, to produce two dimensional images of complex
stellar systems. We detail the determination of the basic observational
reference frame. A technique for recovering model-independent brightness
profiles for data from each occulting edge is discussed, along with the
tomographic combination of these profiles to build an image of the source star.
Finally we demonstrate the technique with recovered images of the {\alpha}
Centauri binary system and the circumstellar environment of the evolved
late-type giant star, Mira.Comment: 8 pages, 8 figures, Accepted by MNRA
On nonsupersymmetric \BC^4/\BZ_N, tachyons, terminal singularities and flips
We investigate nonsupersymmetric \BC^4/\BZ_N orbifold singularities using
their description in terms of the string worldsheet conformal field theory and
its close relation with the toric geometry description of these singularities
and their possible resolutions. Analytic and numerical study strongly suggest
the absence of nonsupersymmetric Type II terminal singularities (i.e. with no
marginal or relevant blowup modes) so that there are always moduli or closed
string tachyons that give rise to resolutions of these singularities, although
supersymmetric and Type 0 terminal singularities do exist. Using gauged linear
sigma models, we analyze the phase structure of these singularities, which
often involves 4-dimensional flip transitions, occurring between resolution
endpoints of distinct topology. We then discuss 4-dim analogs of unstable
conifold-like singularities that exhibit flips, in particular their Type II GSO
projection and the phase structure. We also briefly discuss aspects of
M2-branes stacked at such singularities and nonsupersymmetric AdS_4\times
S^7/\BZ_N backgrounds.Comment: Latex, 43pgs incl. appendices, 2 eps figs, v2. minor clarifications
added, to appear in JHE
Degenerations of toric varieties over valuation rings
We develop a theory of multi-stage degenerations of toric varieties over
finite rank valuation rings, extending the Mumford--Gubler theory in rank one.
Such degenerations are constructed from fan-like structures over totally
ordered abelian groups of finite rank. Our main theorem describes the geometry
of successive special fibers in the degeneration in terms of the polyhedral
geometry of a system of recession complexes associated to the fan.Comment: 13 pages. v3: Added Example 4.1.8 and new references. To appear in
Bulletin of the London Mathematical Societ
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