Let $X$ be a minimal surface of general type and maximal Albanese dimension with irregularity $qgeq 2$. We show that $K_X^2geq 4chi(mathcal O_X)+4(q-2)$ if $K_X^2<frac92chi(mathcal O_X)$, and also obtain the characterization of the equality. As a consequence, we prove a conjecture of Manetti on the geography of irregular surfaces if $K_X^2geq 36(q-2)$ or $chi(mathcal O_X)geq 8(q-2)$, and we also prove a conjecture that surfaces of general type and maximal Albanese dimension with $K_X^2=4chi(mathcal O_X)$ are exactly the resolution of double covers of abelian surfaces branched over ample divisors with at worst simple singularities.
Let $f:,S to B$ be a locally non-trivial relatively minimal fibration of genus $ggeq 2$ with relative irregularity $q_f$. It was conjectured by Barja and Stoppino that the slope $lambda_fgeq frac{4(g-1)}{g-q_f}$. We prove the conjecture when $q_f$ is small with respect to $g$; we also construct counterexamples when $g$ is odd and $q_f=(g+1)/2$.
We prove the non-existence of Shimura subvarieties of positive dimension contained generically in the hyperelliptic Torelli locus for curves of genus at least 8, which is an analogue of Oorts conjecture in the hyperelliptic case.
Let $f:X to mathbb{P}^1$ be a non-isotrivial family of semi-stable curves of genus $ggeq 1$ defined over an algebraically closed field $k$ with $s_{nc}$ singular fibers whose Jacobians are non-compact. We prove that $s_{nc}geq 5$ if $k=mathbb C$ and $ggeq 5$; we also prove that $s_{nc}geq 4$ if ${rm char}~k>0$ and the relative Jacobian of $f$ is non-smooth.
In four classes of materials, the layered copper-oxides, organics, iron-pnictides and heavy-fermion compounds, an unconventional superconducting state emerges as a magnetic transition is tuned toward absolute zero temperature, that is, toward a magnetic quantum-critical point (QCP). In most materials, the QCP is accessed by chemical substitutions or applied pressure. CeCoIn5 is one of the few materials that are born as a quantum-critical superconductor and, therefore, offers the opportunity to explore the consequences of chemical disorder. Cadmium-doped crystals of CeCoIn5 are a particularly interesting case where Cd substitution induces long-range magnetic order, as in Zn-doped copper-oxides. Applied pressure globally supresses the Cd-induced magnetic order and restores bulk superconductivity. Here we show, however, that local magnetic correlations, whose spatial extent decreases with applied pressure, persist at the extrapolated QCP. The residual droplets of impurity-induced magnetic moments prevent the reappearance of conventional signatures of quantum criticality, but induce a heterogeneous electronic state. These discoveries show that spin droplets can be a source of electronic heterogeneity in classes of strongly correlated electron systems and emphasize the need for caution when interpreting the effects of tuning a correlated system by chemical substitution.
We report the temperature-pressure (T-P) phase diagram of CePt2In7 single crystals, especially the pressure evolution of the antiferromagnetic order and the emergence of superconductivity, which have been studied by electrical resistivity and ac calorimetry under nearly hydrostatic environments. Compared with its polycrystalline counterpart, bulk superconductivity coexists with antiferromagnetism in a much narrower pressure region. The possible existence of textured superconductivity and local quantum criticality also are observed in CePt2In7, exhibiting a remarkable similarity with CeRhIn5.
Point-contact Andreev reflection spectroscopy (PCARS) is applied to investigate the gap structure in iron pnictide single crystal superconductors of the AFe_2As_2 (A=Ba, Sr) family (Fe-122). The observed point-contact junction conductance curves, G(V), can be divided into two categories: one where Andreev reflection is present for both (Ba_{0.6}K_{0.4})Fe_2As_2 and Ba(Fe_{0.9}Co_{0.1})_2As_2, and the other with a V^{2/3} background conductance universally observed extending even up to 100 meV for Sr_{0.6}Na_{0.4}Fe_2As_2 and Sr(Fe_{0.9}Co_{0.1})_2As_2. The latter is also observed in point-contact junctions on the nonsuperconducting parent compound BaFe_2As_2. Mesoscopic phase-separated coexistence of magnetic and superconducting orders is considered to explain distinct behaviors in the superconducting samples. For Ba_{0.6}K_{0.4}Fe_2As_2, double peaks due to Andreev reflection with strongly-sloping background are frequently observed for point-contacts on freshly-cleaved c-axis surfaces. If normalized by a background baseline and analyzed by the Blonder-Tinkham-Klapwijk model, the data show a gap size ~3.0-4.0 meV with 2Delta_0/k_BT_c ~ 2.0-2.6, consistent with the smaller gap size reported in the LnFeAsO family (Fe-1111). For the Ba(Fe_{0.9}Co_{0.1})_2As_2, G(V) curves typically display a zero-bias conductance peak.
We study the structure and melting of a classical bilayer system of dipoles, in a setup where the dipoles are oriented perpendicular to the planes of the layers and the density of dipoles is the same in each layer. Due to the anisotropic character of the dipole-dipole interactions, we find that the ground-state configuration is given by two hexagonal crystals positioned on top of each other, independent of the interlayer spacing and dipolar density. For large interlayer distances these crystals are independent, while in the opposite limit of small interlayer distances the system behaves as a two-dimensional crystal of paired dipoles. Within the harmonic approximation for the phonon excitations, the melting temperature of these crystalline configurations displays a non-monotonic dependence on the interlayer distance, which is associated with a re-entrant melting behavior in the form of solid-liquid-solid-liquid transitions at fixed temperature.
