Birational automorphisms of a three-dimensional double quadric with an elementary singularity

It is proved that the group of birational automorphisms of a three-dimensional double quadric with a singular point arising from a double point on the branch divisor is a semidirect product of the free group generated by birational involutions of a special form and the group of regular automorphisms. The proof is based on the method of `untwisting' maximal singularities of linear systems.Comment: 18 page

Birational rigidity of a three-dimensional double cone

It is proved that a three-dimensional double cone is a birationally rigid variety. We also compute the group of birational automorphisms of such a variety. This work is based on the method of "untwisting" maximal singularities of linear system.Comment: 20 pages; AmsLaTe

Mineralogical and geochemical features of the Manus Basin hydrothermal sulfide ores, Bismarck Sea

Paragenetic mineral assemblages have been established based on mineralogical, chemical, and isotope (S, Pb) studies, and the sequence of deposition has been defined in hydrothennal sulfide structures in a typical back-arc basin. The ores in the Manus basin have a prominent Zn specialization (sphalerite, würtzite, and fe-sphalerite). An association of Fe-spbalerite and galena with Ag sulfosalts is noted that is not characteristic of typical midocean ridge hydrothennal systems. The average 34S in the sulfide minerals is 3.5%o, which corresponds to the medium-temperature sphalerite stage in hydrothermal mineral fonnation. It is suggested that the metal source is located in the relatively acid rocks of the island-arc tholeiitic series and possibly in sediments

Extended Magnetic Dome Induced by Low Pressures in Superconducting FeSe1-x_\mathrm{1\text{-}x}Sx_\mathrm{x}

We report muon spin rotation ($\mu$SR) and magnetization measurements under pressure on Fe$_{1+\delta}$Se$_\mathrm{1\text{-}x}$S$_\mathrm{x}$ with x $\approx 0.11$.Above $p\approx0.6$ GPa we find microscopic coexistence of superconductivity with an extended dome of long range magnetic order that spans a pressure range between previously reported separated magnetic phases. The magnetism initially competes on an atomic scale with the coexisting superconductivity leading to a local maximum and minimum of the superconducting $T_\mathrm{c}(p)$. The maximum of $T_\mathrm{c}$ corresponds to the onset of magnetism while the minimum coincides with the pressure of strongest competition. A shift of the maximum of $T_\mathrm{c}(p)$ for a series of single crystals with x up to 0.14 roughly extrapolates to a putative magnetic and superconducting state at ambient pressure for x $\geq0.2$.Comment: 10 pages, 6 figures, including supplemental materia