18,907 research outputs found
On the Seshadri constants of adjoint line bundles
In the present paper we are concerned with the possible values of Seshadri
constants. While in general every positive rational number appears as the local
Seshadri constant of some ample line bundle, we point out that for adjoint line
bundles there are explicit lower bounds depending only on the dimension of the
underlying variety. In the surface case, where the optimal lower bound is 1/2,
we characterize all possible values in the range between 1/2 and 1 -- there are
surprisingly few. As expected, one obtains even more restrictive results for
the Seshadri constants of adjoints of very ample line bundles. Our description
of the border case in this situation makes use of adjunction-theoretical
results on surfaces. Finally, we study Seshadri constants of adjoint line
bundles in the multi-point setting.Comment: Added Remark 3.3, which points out an improvement to the lower bound
in Theorem 3.2 by using G. Heier's resul
Nonlocal electron-phonon interaction as a source of dynamic charge stripes in the cuprates
We calculate for La2CuO4 the phonon-induced redistribution of the electronic
charge density in the insulating, the underdoped pseudogap and the more
conventional metallic state as obtained for optimal and overdoping,
respectively. The investigation is performed for the anomalous
high-frequency-oxygen-bond stretching modes (OBSM) which experimentally are
known to display a strong softening of the frequencies upon doping in the
cuprates. This most likely generic anomalous behaviour of the OBSM has been
shown to be due to a strong nonlocal electron-phonon interaction (EPI) mediated
by charge fluctuations on the ions. The modeling of the competing electronic
states of the cuprates is achieved in terms of consecutive orbital selective
incompressibility-compressibility transitions for the charge response. We
demonstrate that the softening of the OBSM in these states is due to nonlocally
induced dynamic charge inhomogenities in form of charge stripes along the CuO
bonds with different orbital character. Thus, a multi-orbital approach is
essential for the CuO plane. The dynamic charge inhomogeneities may in turn be
considered as precursors of static charge stripe order as recently observed in
LaBaCuO in a broad range of doping around x=1/8. The latter
may trigger a reconstruction of the Fermi surface into small pockets with
reduced doping. We argue that the incompressibility of the Cu3d orbital and
simultaneously the compressibility of the O2p orbital in the pseudogap state
seems to be required to nucleate dynamic stripes.Comment: 10 pages, 4 figures, to be published in "Advances in Condensed Matter
Physics
Seshadri constants on the self-product of an elliptic curve
The purpose of this paper is to study Seshadri constants on the self-product
of an elliptic curve . We provide explicit formulas for
computing the Seshadri constants of all ample line bundles on the surfaces
considered. As an application, we obtain a good picture of the behaviour of the
Seshadri function on the nef cone
Seshadri constants and the generation of jets
In this paper we explore the connection between Seshadri constants and the
generation of jets. It is well-known that one way to view Seshadri constants is
to consider them as measuring the rate of growth of the number of jets that
multiples of a line bundle generate. Here we ask, conversely, what we can say
about the number of jets once the Seshadri constant is known. As an application
of our results, we prove a characterization of projective space among all Fano
varieties in terms of Seshadri constants
Prospect Theory Goes to War: Loss-Aversion and the Duration of Military Combat
This paper contributes to the empirical foundation of prospect theory in real-life international relations by testing two of its major implications in the field of military conflict. Using duration analysis for a data set of twentieth century battles, it is shown how the experience of losses contributes positively to the preparedness to continue fighting, up to a point where casualties clearly outweigh any direct utility drawn from ordinary expected-utility theory. Moreover, the empirical results also indicate that the relative position compared to the opponent's is clearly less important for the decision whether to stop a battle or not than the change of one's own position compared to the beginning of the fight
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