167 research outputs found
Obstructions to the Existence of Sasaki-Einstein Metrics
We describe two simple obstructions to the existence of Ricci-flat Kahler
cone metrics on isolated Gorenstein singularities or, equivalently, to the
existence of Sasaki-Einstein metrics on the links of these singularities. In
particular, this also leads to new obstructions for Kahler-Einstein metrics on
Fano orbifolds. We present several families of hypersurface singularities that
are obstructed, including 3-fold and 4-fold singularities of ADE type that have
been studied previously in the physics literature. We show that the AdS/CFT
dual of one obstruction is that the R-charge of a gauge invariant chiral
primary operator violates the unitarity bound.Comment: 35 pages, 1 figure; references and a footnote adde
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
A global invariant for three dimensional CR-manifolds
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46621/1/222_2005_Article_BF01404456.pd
On Sasaki-Einstein manifolds in dimension five
We prove the existence of Sasaki-Einstein metrics on certain simply connected
5-manifolds where until now existence was unknown. All of these manifolds have
non-trivial torsion classes. On several of these we show that there are a
countable infinity of deformation classes of Sasaki-Einstein structures.Comment: 18 pages, Exposition was expanded and a reference adde
Szeg\"o kernel asymptotics and Morse inequalities on CR manifolds
We consider an abstract compact orientable Cauchy-Riemann manifold endowed
with a Cauchy-Riemann complex line bundle. We assume that the manifold
satisfies condition Y(q) everywhere. In this paper we obtain a scaling
upper-bound for the Szeg\"o kernel on (0, q)-forms with values in the high
tensor powers of the line bundle. This gives after integration weak Morse
inequalities, analogues of the holomorphic Morse inequalities of Demailly. By a
refined spectral analysis we obtain also strong Morse inequalities which we
apply to the embedding of some convex-concave manifolds.Comment: 40 pages, the constants in Theorems 1.1-1.8 have been modified by a
multiplicative constant 1/2 ; v.2 is a final updat
Low-field magnetoresistance in GaAs 2D holes
We report low-field magnetotransport data in two-dimensional hole systems in
GaAs/AlGaAs heterostructures and quantum wells, in a large density range, cm, with primary focus on
samples grown on (311)A GaAs substrates. At high densities, cm, we observe a remarkably strong positive magnetoresistance.
It appears in samples with an anisotropic in-plane mobility and predominantly
along the low-mobility direction, and is strongly dependent on the
perpendicular electric field and the resulting spin-orbit interaction induced
spin-subband population difference. A careful examination of the data reveals
that the magnetoresistance must result from a combination of factors including
the presence of two spin-subbands, a corrugated quantum well interface which
leads to the mobility anisotropy, and possibly weak anti-localization. None of
these factors can alone account for the observed positive magnetoresistance. We
also present the evolution of the data with density: the magnitude of the
positive magnetoresistance decreases with decreasing density until, at the
lowest density studied ( cm), it vanishes and is
replaced by a weak negative magnetoresistance.Comment: 8 pages, 8 figure
Lojasiewicz exponent of families of ideals, Rees mixed multiplicities and Newton filtrations
We give an expression for the {\L}ojasiewicz exponent of a wide class of
n-tuples of ideals in \O_n using the information given by a
fixed Newton filtration. In order to obtain this expression we consider a
reformulation of {\L}ojasiewicz exponents in terms of Rees mixed
multiplicities. As a consequence, we obtain a wide class of semi-weighted
homogeneous functions for which the
{\L}ojasiewicz of its gradient map attains the maximum possible
value.Comment: 25 pages. Updated with minor change
Holographic Uniformization
We derive and study supergravity BPS flow equations for M5 or D3 branes
wrapping a Riemann surface. They take the form of novel geometric flows
intrinsically defined on the surface. Their dual field-theoretic interpretation
suggests the existence of solutions interpolating between an arbitrary metric
in the UV and the constant-curvature metric in the IR. We confirm this
conjecture with a rigorous global existence proof.Comment: 52 pages, 3 figure
- …