On the second exterior power of tangent bundles of Fano fourfolds with Picard number rho(X)geqslant2rho(X)geqslant2

In this paper, we classify Fano fourfolds whose the second exterior power of tangent bundles are numerically effective with Picard number greater than one.Comment: 14 pages, v2: minor chang

On projective space bundle with nef normalized tautological divisor

In this paper, we study the structure of projective space bundles whose relative anti-canonical line bundle is nef. As an application, we get a characterization of abelian varieties up to finite etale covering.Comment: 12 page

On the second and third exterior power of tangent bundles of Fano manifolds with birational contractions

In this paper, we classify Fano manifolds with elementary contractions of birational type such that the second or third exterior power of tangent bundles are numerically effective.Comment: 10 page

On the classification of rank 2 almost Fano bundles on projective space

An almost Fano bundle is a vector bundle on a smooth projective variety that its projectivization is an almost Fano variety. In this paper, we prove that almost Fano bundles exist only on almost Fano manifolds and study rank 2 almost Fano bundles over projective spaces.Comment: 11 page

Classification of log del Pezzo surfaces of index three

A normal projective non-Gorenstein log-terminal surface $S$ is called a log del Pezzo surface of index three if the three-times of the anti-canonical divisor $-3K_S$ is an ample Cartier divisor. We classify all of the log del Pezzo surfaces of index three. The technique for the classification based on the argument of Nakayama.Comment: 68 page

Mixed phases during the phase transitions

Quest for a new form of matter inside compact stars compels us to examine the thermodynamical properties of the phase transitions. We closely consider the first-order phase transitions and the phase equilibrium on the basis of the Gibbs conditions, taking the liquid-gas phase transition in asymmetric nuclear matter as an example. Characteristic features of the mixed phase are figured out by solving the coupled equations for mean-fields and densities of constituent particles self-consistently within the Thomas-Fermi approximation. The mixed phase is inhomogeneous matter composed of two phases in equilibrium; it takes a crystalline structure with a unit of various geometrical shapes, inside of which one phase with a characteristic shape, called "pasta", is embedded in another phase by some volume fraction. This framework enables us to properly take into account the Coulomb interaction and the interface energy, and thereby sometimes we see the mechanical instability of the geometric structures of the mixed phase. Thermal effect on the liquid-gas phase transition is also elucidated. Similarly hadron-quark deconfinement transition is studied in hyperonic matter, where the neutrino-trapping effect as well as the thermal effect is discussed in relation to the properties of the mixed phase. Specific features of the mixed phase are elucidated and the equation of state is presented.Comment: 33 pages,20 figures, to appear in the book "Neutron Stars: the aspects of high density matter, equations of state and related observables" by NOVA scientific pu

Equation of State of Structured Matter at Finite Temperature

We investigate the properties of nuclear matter at the first-order phase transitions such as liquid-gas phase transition and hadron-quark phase transition. As a general feature of the first-order phase transitions of matter consisting of many species of charged particles, there appears a mixed phases with geometrical structures called ``pasta'' due to the balance of the Coulomb repulsion and the surface tension between two phases. The equation of state (EOS) of mixed phase is different from the one obtained by a bulk application of the Gibbs conditions or by the Maxwell construction due to the effects of the non-uniform structure. We show that the charge screening and strong surface tension make the EOS close to that of the Maxwell construction. The thermal effects are elucidated as well as the above finite-size effects.Comment: Presentation at NFQCD 2010 at Yukawa Inst. TO appear on Prog. Theor. Phys. Supp

A Novel Formulation by Lagrangian Variational Principle for Rotational Equilibria: Toward Multi-Dimensional Stellar Evolutions

We have developed a new formulation to obtain self-gravitating, axisymmetric configurations in permanent rotation. The formulation is based on the Lagrangian variational principle, and treats not only barotropic but also baroclinic equations of state, for which angular momentum distributions are not necessarily cylindrical. We adopt a Monte Carlo technique, which is analogous to those employed in other fields, e.g. nuclear physics, in minimizing the energy functional, which is evaluated on a triangulated mesh. This letter is a proof of principle and detailed comparisons with existing results will be reported in the sequel, but some test calculations are presented, in which we have achieved an error of $O(10^{-4})$ in the Virial relation. We have in mind the application of this method to two-dimensional calculations of the evolutions of rotating stars, for which the Lagrangian formulation is best suited.Comment: 5 pages, 2 figures, accepted for publishing in MNRAS Letter

Hot hadron-quark mixed phase including hyperons

We study the hadron-quark phase transition with the finite size effects at finite temperature. For the hadron phase, we adopt a realistic equation of state in the framework of the Brueckner-Hartree-Fock theory including hyperons. The properties of the mixed phase are clarified by considering the finite size effects under the Gibbs conditions. We find that the equation of state becomes softer than that at zero-temperature for some density region. We also find that the equation of state gets closer to that given by the Maxwell construction. Moreover, the number of hyperons is suppressed by the presence of quarks. These are characteristic features of the hadron-quark mixed phase, and should be important for many astrophysical phenomena such as mergers of binary neutron stars.Comment: 8 pages, 13 figures. accepted to Phys. Rev.

Finite size effects in hadron-quark phase transition by the Dyson-Schwinger method

We study the hadron-quark phase transition, taking into account the finite-size effects for neutron star matter. For the hadron phase, we adopt a realistic equation of state within the framework of the Brueckner-Hartree-Fock theory. For the quark phase, we apply the Dyson-Schwinger method. The properties of the mixed phase are clarified by considering the finite-size effects. We find that, if the surface tension is strong enough, the equation of state becomes to be close the one with the Maxwell condition, though we properly adopt the Gibbs conditions. This result is qualitatively the same with the one by the use of the simple bag model. We also find that the mass-radius relation by the EoS is consistent with the observations of massive neutron stars.Comment: 4 pages, 2 figures, the proceeding for "Nuclear Physics in Astrophysics VI