Birational automorphism groups of projective varieties of Picard number two

We slightly extend a result of Oguiso on birational or automorphism groups (resp. of Lazi\'c - Peternell on Morrison-Kawamata cone conjecture) from Calabi-Yau manifolds of Picard number two to arbitrary singular varieties X (resp. to klt Calabi-Yau pairs in broad sense) of Picard number two. When X has only klt singularities and is not a complex torus, we show that either Aut(X) is almost cyclic, or it has only finitely many connected components.Comment: title slightly changed to this; some proof simplified; submitted to the Proceedings of Groups of Automorphisms in Birational and Affine Geometry, 28 October - 3 November 2012, C.I.R.M., Trento, Ital

Termination of (many) 4-dimensional log flips

We prove that any sequence of 4-dimensional log flips that begins with a klt pair (X,D) such that -(K+D) is numerically equivalent to an effective divisor, terminates. This implies termination of flips that begin with a log Fano pair and termination of flips in a relative birational setting. We also prove termination of directed flips with big K+D. As a consequence, we prove existence of minimal models of 4-dimensional dlt pairs of general type, existence of 5-dimensional log flips, and rationality of Kodaira energy in dimension 4.Comment: 13 pages; a minor change in the proof of Thm.4.

Novel Electronic State and Superconductivity in the Electron-Doped High-Tc T'-Superconductors

In this review article, we show our recent results relating to the undoped (Ce-free) superconductivity in the electron-doped high-Tc cuprates with the so-called T' structure. For an introduction, we briefly mention the characteristics of the electron-doped T'-cuprates, including the reduction annealing, conventional phase diagram and undoped superconductivity. Then, our transport and magnetic results and results relating to the superconducting pairing symmetry of the undoped and underdoped T'-cuprates are shown. Collaborating spectroscopic and nuclear magnetic resonance results are also shown briefly. It has been found that, through the reduction annealing, a strongly localized state of carriers accompanied by an antiferromagnetic pseudogap in the as-grown samples changes to a metallic and superconducting state with a short-range magnetic order in the reduced superconducting samples. The formation of the short-range magnetic order due to a very small amount of excess oxygen in the reduced superconducting samples suggests that the T'-cuprates exhibiting the undoped superconductivity in the parent compounds are regarded as strongly correlated electron systems, as well as the hole-doped high-Tc cuprates. We show our proposed electronic structure model to understand the undoped superconductivity. Finally, unsolved future issues of the T'-cuprates are discussed.Comment: 13 pages, 8 figure

Development of Cu-spin correlation in Bi_1.74_Pb_0.38_Sr_1.88_Cu_1-y_Zn_y_O_6+d_ high-temperature superconductors observed by muon spin relaxation

A systematic muon-spin-relaxation study in Bi-2201 high-Tc cuprates has revealed for the first time that the Cu-spin correlation (CSC) is developed at low temperatures below 2 K in a wide range of hole concentration where superconductivity appears. The CSC tends to become weak gradually with increasing hole-concentration. Moreover, CSC has been enhanced through the 3% substitution of Zn for Cu. These results are quite similar to those observed in La-214 high-Tc cuprates. Accordingly, it has been suggested that the intimate relation between the so-called spin-charge stripe correlations and superconductivity is a universal feature in hole-doped high-Tc cuprates. Furthermore, apparent development of CSC, which is suppressed through the Zn substitution oppositely, has been observed in non-superconducting heavily overdoped samples, being argued in the context of a recently proposed ferromagnetic state in heavily overdoped cuprates.Comment: 6 pages, 5 figure

Characterization of the 4-canonical birationality of algebraic threefolds

In this article we present a 3-dimensional analogue of a well-known theorem of E. Bombieri (in 1973) which characterizes the bi-canonical birationality of surfaces of general type. Let $X$ be a projective minimal 3-fold of general type with $\mathbb{Q}$-factorial terminal singularities and the geometric genus $p_g(X)\ge 5$. We show that the 4-canonical map $\phi_4$ is {\it not} birational onto its image if and only if $X$ is birationally fibred by a family $\mathscr{C}$ of irreducible curves of geometric genus 2 with $K_X\cdot C_0=1$ where $C_0$ is a general irreducible member in $\mathscr{C}$.Comment: 25 pages, to appear in Mathematische Zeitschrif

Hole-trapping by Ni, Kondo effect and electronic phase diagram in non-superconducting Ni-substituted La2-xSrxCu1-yNiyO4

In order to investigate the electronic state in the normal state of high-Tc cuprates in a wide range of temperature and hole-concentration, specific-heat, electrical-resistivity, magnetization and muon-spin-relaxation (muSR) measurements have been performed in non-superconducting Ni-substituted La2-xSrxCu1-yNiyO4 where the superconductivity is suppressed through the partial substitution of Ni for Cu without disturbing the Cu-spin correlation in the CuO2 plane so much. In the underdoped regime, it has been found that there exist both weakly localized holes around Ni and itinerant holes at high temperatures. With decreasing temperature, all holes tend to be localized, followed by the occurrence of variable-range hopping conduction at low temperatures. Finally, in the ground state, it has been found that each Ni2+ ion traps a hole strongly and that a magnetically ordered state appears. In the overdoped regime, on the other hand, it has been found that a Kondo-like state is formed around each Ni2+ spin at low temperatures. In conclusion, the ground state of non-superconducting La2-xSrxCu1-yNiyO4 changes upon hole doping from a magnetically ordered state with the strong hole-trapping by Ni2+ to a metallic state with Kondo-like behavior due to Ni2+ spins, and the quantum phase transition is crossover-like due to the phase separation into short-range magnetically ordered and metallic regions.Comment: 9 pages, 8 figures, accepted for publication in Phys. Rev.