Related papers: Quartic double solids with icosahedral symmetry
We study quartic surfaces that admit a group of projective automorphisms isomorphic to icosahedron group.
We study equivariant birational geometry of (rational) quartic double solids ramified over (singular) Kummer surfaces.
We study the surface of Gauss double points associated to a very general quartic surface and the natural morphisms associated to it.
We study the rationality problem for nodal quartic double solids. In particular, we prove that nodal quartic double solids with at most six singular points are irrational, and nodal quartic double solids with at least eleven singular points…
We show that the variable cohomology of a general complete intersection of quadrics can be identified with the intersection cohomology of a double covering. As a consequence, we show that the middle cohomology of a general complete…
We construct examples of nodal quartic double solids that admit uniformly rational, and so elliptic in Gromov' sense, small algebraic resolutions.
We study the mixed Hodge structure on the third homology group of a threefold which is the double cover of projective three-space ramified over a quartic surface with a double conic. We deal with the Torelli problem for such threefolds.
We study the congruence of bitangent lines of an irreducible surface in the 3-dimensional projective space in arbitrary characteristic, with special attention to quartic surfaces with rational double points and, in particular, Kummer…
We discuss an unusual phenomenon in (integral) positive ternary quadratic forms. We also describe an interesting pairing of genera of ternary forms.
Using a quartic surface and its rational curves we can give an infinite number of integer hexahedra; these are 6 sided 3d solids, each face a trapezoid, with all sides and diagonals having intger lengths.
This letter presents a study on the stability of the 12-fold symmetry soft-matter quasicrystals from the angle of thermodynamics combining dynamics of the matter. The results are quantitative, which depend upon only the material constants…
We investigate the idea that the double cover of the rotational icosahedral symmetry group is the family symmetry group in the quark sector. The icosahedral (A5) group was previously proposed as a viable family symmetry group for the…
Quadric complexes are square complexes satisfying a certain combinatorial nonpositive curvature condition. These complexes generalize 2-dimensional CAT(0) cube complexes and are a square analog of systolic complexes. We introduce and study…
We classify rational, irreducible quartic symmetroids in projective 3-space. They are either singular along a line or a smooth conic section, or they have a triple point or a tacnode.
The stability of the hard-sphere icosahedral quasilattice is analyzed using the differential formulation of the generalized effective liquid approximation. We find that the icosahedral quasilattice is metastable with respect to the…
We prove some symmetric $q$-congruences.
Quark-hadron duality and its potential applications are discussed. We focus on theoretical efforts to model duality.
Generalizing the octahedral configuration of six congruent cylinders touching the unit sphere, we exhibit configurations of congruent cylinders associated to a pair of dual Platonic bodies.
We investigate quasicrystal-forming soft matter using a two-scale phase field crystal model. At state points near thermodynamic coexistence between bulk quasicrystals and the liquid phase, we find multiple metastable spatially localized…
We study the geometry and codes of quartic surfaces with many cusps. We apply Gr\"obner bases to find examples of various configurations of cusps on quartics.