8 research outputs found
Weakly--exceptional quotient singularities
A singularity is said to be weakly--exceptional if it has a unique purely log
terminal blow up. In dimension , V. Shokurov proved that weakly--exceptional
quotient singularities are exactly those of types , , ,
. This paper classifies the weakly--exceptional quotient singularities
in dimensions and
Existence of Kähler–Einstein metrics and multiplier ideal sheaves on del Pezzo surfaces
We apply Nadel’s method of multiplier ideal sheaves to show that every complex del Pezzo surface of degree at most six whose automorphism group acts without fixed points has a Kähler–Einstein metric. In particular, all del Pezzo surfaces of degree 4, 5, or 6 and certain special del Pezzo surfaces of lower degree are shown to have a Kähler–Einstein metric. These existence statements are not new, but the proofs given in the present paper are less involved than earlier ones by Siu, Tian and Tian–Yau
Interacting Preformed Cooper Pairs in Resonant Fermi Gases
We consider the normal phase of a strongly interacting Fermi gas, which can
have either an equal or an unequal number of atoms in its two accessible spin
states. Due to the unitarity-limited attractive interaction between particles
with different spin, noncondensed Cooper pairs are formed. The starting point
in treating preformed pairs is the Nozi\`{e}res-Schmitt-Rink (NSR) theory,
which approximates the pairs as being noninteracting. Here, we consider the
effects of the interactions between the Cooper pairs in a Wilsonian
renormalization-group scheme. Starting from the exact bosonic action for the
pairs, we calculate the Cooper-pair self-energy by combining the NSR formalism
with the Wilsonian approach. We compare our findings with the recent
experiments by Harikoshi {\it et al.} [Science {\bf 327}, 442 (2010)] and
Nascimb\`{e}ne {\it et al.} [Nature {\bf 463}, 1057 (2010)], and find very good
agreement. We also make predictions for the population-imbalanced case, that
can be tested in experiments.Comment: 10 pages, 6 figures, accepted version for PRA, discussion of the
imbalanced Fermi gas added, new figure and references adde
Sous-groupes alg\'ebriques du groupe de Cremona
We give a complete classification of maximal algebraic subgroups of the
Cremona group of the plane and provide algebraic varieties that parametrize the
conjugacy classes.
-----
Nous donnons une classification compl\`ete des sous-groupes alg\'ebriques
maximaux du groupe de Cremona du plan et explicitons les vari\'et\'es qui
param\`etrent les classes de conjugaison.Comment: Text in French, Translated introduction, 35 pages, 1 figure, to
appear in Transform. Group