7,578 research outputs found
Bertini theorems for F-singularities
We prove that strongly F-regular and F-pure singularities satisfy
Bertini-type theorems (including in the context of pairs) by building upon a
framework of Cumino, Greco and Manaresi (compare with the work of Jouanolou and
Spreafico). We also prove that F-injective singularities fail to satisfy even
the most basic Bertini-type results.Comment: Typos corrected and other minor changes. To appear in the Proceedings
of the London Mathematical Societ
Spontaneous emission of polaritons from a Bose-Einstein condensate
We study the spontaneous emission of a partially excited Bose-Einstein
condensate composed of two-level atoms. The formation of polaritons induced by
the ground-state part of the condensate leads to an avoided crossing in the
photon spectrum. This avoided crossing acts similarly to a photonic band gap
and modifies the spontaneous emission rate.Comment: 4 pages, 2 figures, revte
F-singularities in families
We study the behavior of test ideals and F-singularities in families. In
particular, we obtain generic (and non-generic) restriction theorems for test
ideals and non-F-pure ideals. Additionally, we study the global behavior of
certain canonical linear systems (induced by Frobenius) associated to adjoint
line bundles, in families. As a consequence, we obtain some positivity results
for pushforwards of some adjoint line bundles and for certain subsheaves of
these.Comment: 60 pages, typos corrected throughout and improved exposition, to
appear in Algebraic Geometr
Discreteness and rationality of -jumping numbers on singular varieties
We prove that the -jumping numbers of the test ideal \tau(X; \Delta,
\ba^t) are discrete and rational under the assumptions that is a normal
and -finite variety over a field of positive characteristic ,
is \bQ-Cartier of index not divisible , and either is
essentially of finite type over a field or the sheaf of ideals \ba is locally
principal. This is the largest generality for which discreteness and
rationality are known for the jumping numbers of multiplier ideals in
characteristic zero.Comment: 29 pages, minor changes, to appear in Mathematische Annale
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