Real quadrics of codimension 3 in $ \mathbb C^6$ and their non-linear automorphisms

Abstract

We have carried out pseudopotential calculations of the effect of mixing in semiconductor superlattices between bulk states derived from the conduction band minimum at thecentreof the bulk Brillouinzoneand thoseoftheXminimaat thezone edges. Wepresent a systematic account of (i) the strength of this coupling in GaAh4I.4~ superlattices as a function of the layer widths, (ii) the variation as a function of layer width of the magnitude of the energy gap that occurs when the levels derived from different bulk valleys cross, (iii) the changeoftheoscillatorstrengthofthe transitionacross thesuperlattice gapasafunction of the separation of the interacting levels, and (iv) the magnitude of the effect of strain on valley mixing.

On holomorphic automorphisms of a class of non-homogeneous rigid hypersurfaces in ℂ N+1

“…For higher codimension, it is known that each (3, 3)-quadric possessing non-linear automorphisms is equivalent to one of eight quadrics (cf. [13,14]), whose automorphism groups are determined in [1]. For higher degree model surface, Beloshapka considered the surface Q 3 in the space C n ⊕ C n 2 ⊕ C k with coordinates (z ∈ C n , w 2 ∈ C n 2 , w 3 ∈ C k ), given by the equations Im w 2 = z, z , Im w 3 = 2 Re Φ(z, z), where z, z is an n 2 scalar linearly independent Hermitian form, and Φ(z, z) is a homogeneous C k -valued form of degree three, and gave the structure of the automorphism algebra of the cubic (cf.…”