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

Seshadri constants on the self-product of an elliptic curve

The purpose of this paper is to study Seshadri constants on the self-product $E\times E$ of an elliptic curve $E$. 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

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 La$_{2-x}$Ba$_{x}$CuO$_{4}$ 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