2,597 research outputs found
Derived categories of Burniat surfaces and exceptional collections
We construct an exceptional collection of maximal possible length
6 on any of the Burniat surfaces with , a 4-dimensional family of
surfaces of general type with . We also calculate the DG algebra of
endomorphisms of this collection and show that the subcategory generated by
this collection is the same for all Burniat surfaces.
The semiorthogonal complement of is an "almost
phantom" category: it has trivial Hochschild homology, and K_0(\mathcal
A)=\bZ_2^6.Comment: 15 pages, 1 figure; further remarks expande
Semiorthogonal decompositions of derived categories of equivariant coherent sheaves
Let X be an algebraic variety with an action of an algebraic group G. Suppose
X has a full exceptional collection of sheaves, and these sheaves are invariant
under the action of the group. We construct a semiorthogonal decomposition of
bounded derived category of G-equivariant coherent sheaves on X into
components, equivalent to derived categories of twisted representations of the
group. If the group is finite or reductive over the algebraically closed field
of zero characteristic, this gives a full exceptional collection in the derived
equivariant category. We apply our results to particular varieties such as
projective spaces, quadrics, Grassmanians and Del Pezzo surfaces.Comment: 28 pages, uses XY-pi
Stability of Landau-Ginzburg branes
We evaluate the ideas of Pi-stability at the Landau-Ginzburg point in moduli
space of compact Calabi-Yau manifolds, using matrix factorizations to B-model
the topological D-brane category. The standard requirement of unitarity at the
IR fixed point is argued to lead to a notion of "R-stability" for matrix
factorizations of quasi-homogeneous LG potentials. The D0-brane on the quintic
at the Landau-Ginzburg point is not obviously unstable. Aiming to relate
R-stability to a moduli space problem, we then study the action of the gauge
group of similarity transformations on matrix factorizations. We define a naive
moment map-like flow on the gauge orbits and use it to study boundary flows in
several examples. Gauge transformations of non-zero degree play an interesting
role for brane-antibrane annihilation. We also give a careful exposition of the
grading of the Landau-Ginzburg category of B-branes, and prove an index theorem
for matrix factorizations.Comment: 46 pages, LaTeX, summary adde
Derived Categories of Coherent Sheaves and Triangulated Categories of Singularities
In this paper we establish an equivalence between the category of graded
D-branes of type B in Landau-Ginzburg models with homogeneous superpotential W
and the triangulated category of singularities of the fiber of W over zero. The
main result is a theorem that shows that the graded triangulated category of
singularities of the cone over a projective variety is connected via a fully
faithful functor to the bounded derived category of coherent sheaves on the
base of the cone. This implies that the category of graded D-branes of type B
in Landau-Ginzburg models with homogeneous superpotential W is connected via a
fully faithful functor to the derived category of coherent sheaves on the
projective variety defined by the equation W=0.Comment: 26 pp., LaTe
Bound, virtual and resonance -matrix poles from the Schr\"odinger equation
A general method, which we call the potential -matrix pole method, is
developed for obtaining the -matrix pole parameters for bound, virtual and
resonant states based on numerical solutions of the Schr\"odinger equation.
This method is well-known for bound states. In this work we generalize it for
resonant and virtual states, although the corresponding solutions increase
exponentially when . Concrete calculations are performed for the
ground and the first excited states of , the resonance
states (, ), low-lying states of and
, and the subthreshold resonances in the proton-proton system. We
also demonstrate that in the case the broad resonances their energy and width
can be found from the fitting of the experimental phase shifts using the
analytical expression for the elastic scattering -matrix. We compare the
-matrix pole and the -matrix for broad resonance in
Comment: 14 pages, 5 figures (figures 3 and 4 consist of two figures each) and
4 table
Interlayer tunneling spectroscopy of graphite at high magnetic field oriented parallel to the layers
Interlayer tunneling in graphite mesa-type structures is studied at a strong
in-plane magnetic field up to 55 T and low temperature K. The
tunneling spectrum vs. has a pronounced peak at a finite voltage
. The peak position increases linearly with . To explain the
experiment, we develop a theoretical model of graphite in the crossed electric
and magnetic fields. When the fields satisfy the resonant condition
, where is the velocity of the two-dimensional Dirac electrons in
graphene, the wave functions delocalize and give rise to the peak in the
tunneling spectrum observed in the experiment.Comment: 6 pages, 6 figures; corresponds to the published version in Eur.
Phys. J. Special Topics, Proceedings of the IMPACT conference 2012,
http://lptms.u-psud.fr/impact2012
Storage-ring measurement of the hyperfine induced 47Ti18+(2s 2p 3P0 -> 2s2 1S0) transition rate
The hyperfine induced 2s 2p 3P0 > 2s2 1S0 transition rate AHFI in
berylliumlike 47Ti18+ was measured. Resonant electron-ion recombination in a
heavy-ion storage ring was employed to monitor the time dependent population of
the 3P0 state. The experimental value AHFI=0.56(3)/s is almost 60% larger than
theoretically predicted.Comment: 4 pages. 3 figures, 1 table, accepted for publication in Physical
Review Letter
Instanton bundles on Fano threefolds
We introduce the notion of an instanton bundle on a Fano threefold of index
2. For such bundles we give an analogue of a monadic description and discuss
the curve of jumping lines. The cases of threefolds of degree 5 and 4 are
considered in a greater detail.Comment: 31 page, to appear in CEJ
Structure of 2-Methyl-5,6,7-triphenyl-6,7-dihydropyrazolo[2,3-\u3cem\u3ea\u3c/em\u3e]pyrimidine
C25H21N3, Mr = 363.46, monoclinic, P21/n, a = 9.245 (2), b = 23.502 (5), c = 9.340 (2) Å, β= 103.50(3)°, V=1973.3(2) Å3, Z=4, Dx= 1.220 (2) g cm-3, λ (Mo Kα )= 0.71069 Å, μ = 0.068 cm-1, F(000) = 768, T= 292 K, R = 0.091 for 1442 unique observed reflections. The dihydropyrimidine ring adopts a distorted sofa conformation. The aryl substituents on the saturated C atoms have an axial orientation
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