Compact complex homogeneous manifolds with large automorphism groups

Let X be a compact complex homogeneous manifold and let Aut(X) be the complex Lie group of holomorphic automorphisms of X. It is well-known that the dimension of Aut(X) is bounded by an integer that depends only on n=dim X. Moreover, if X is K?hler then dimAut (X)≤n(n+2) with equality only when X is complex projective space. In this article examples of non-K?hler compact complex homogeneous manifolds X are given that demonstrate dimAut(X) can depend exponentially on n. Let X be a connected compact complex manifold of dimension n. The group of holomorphic automorphisms of X, Aut(X), is a complex Lie group [3]. For a fixed n>1, the dimension of Aut(X) can be arbitrarily large compared to n. Simple examples are provided by the Hirzebruch surfaces F _m , m∈N, for which dimAut(F _m )=m+5, see, e.g. [2, Example 2.4.2]. If X is homogeneous, that is, any point of X can be mapped to any other point of X under a holomorphic automorphism, then the dimension of the automorphism group of X is bounded by an integer that depends only on n, see [1, 2, 6]. The estimate given in [2, Theorem 3.8.2] is roughly dimAut(X)≤(n+2) ⁿ . For many classes of manifolds, however, the dimension of the automorphism group never exceeds n(n+2). For example, it follows directly from the classification given by Borel and Remmert [4], that if X is a compact homogeneous K?hler manifold, then dimAut(X)≤n(n+2) with equality only when X is complex projective space P ⁿ . It is an old question raised by Remmert, see [2, p. 99], [6], whether this same bound applies to all compact complex homogeneous manifolds. In this note we show that this is not the case by constructing non-K?hler compact complex homogeneous manifolds whose automorphism group has a dimension that depends exponentially on n. The simplest case among these examples has n=3m+1 and dimAut(X)=3m+3 ^m , so the above conjectured bound is exceeded when n≥19. These manifolds have the structure of non-trivial fiber bundles over products of flag manifolds with parallelizable fibers given as the quotient of a solvable group by a discrete subgroup. They are constructed using the original ideas of Otte [6, 7] and are surprisingly similar to examples found there. Generally, a product of manifolds does not result in an automorphism group with a large dimension relative to n. Nevertheless, products are used in an essential way in the construction given here, and it is perhaps this feature that caused such examples to be previously overlooked. Oblatum 13-X-97 & 24-X-1997     

An ESR study of the acetaldehyde radical cation in freon matrices: Evidence for halogen superhyperfine interaction

The substructure associated with the doublet ESR spectrum of the acetaldehyde radical cation in Freon matrices below 100 K is shown to arise from a matrix interaction and not, as previously proposed, from coupling to the hydrogens of the methyl group. Since the reversible loss of this substructure at higher temperature is accompanied by almost no change in the large isotropic ¹H coupling(136 G) to the aldehydic hydrogen, the matrix perturbation appears to have a negligible effect on the spin distribution in the radical cation and is according interpreted as a superhyperfine interaction     

Light emission from porous silicon single and multiple cavities

Experimental and theoretical techniques are used to examine the effects of microstructuring on the optical properties of multilayer, single and multiple microcavity structures fabricated from porous silicon. Measurements of the reflectivity and photoluminescence spectra of three multilayer samples are presented. The results are modelled using a transfer matrix technique including a negative absorption term to represent the effect of spontaneous emission which gives luminescence. The emitted light is strongly controlled by the optical modes of the structures and very good agreement is observed between theory and experiment.     

Primary electron reflections in discharges surrounded by magnetic multipole walls

By observing the primary electron trajectories and studying experimentally the equilibrium of an argon plasma in the pressure range 0.8 × 10^?4 – 8 × 10^?4 torr, we show that the main effect of the surrounding magnetic wall is not the confinement of the plasma but the confinement of the primary electrons in the discharge.     

Triangular actions onC 3

Free algebraic actions of a connected algebraic groupG onC ³ which can be triangularized are shown to be trivial, that isC ³ is equivariantly isomorphic toGxC ^3–dimG . This result follows directly from the case of the additive groupG=G _a and is shown to hold for quasi-algebraic actions as well. Connections with the classification of homogeneous affine varieties are discussed.Partially supported by NSF grant DMS 8420315     

Subdirect products of hereditary congruence lattices

A congruence lattice L of an algebra A is called power-hereditary if every 0-1 sublattice of Lⁿ is the congruence lattice of an algebra on Aⁿ for all positive integers n. Let A and B be finite algebras. We prove

Compressibility of copper via the self-consistent APW method

The self-consistent APW method was used in determining pressure as a function of volume for f.c.c. copper. The results are in excellent agreement in the range 0 to 600 kbar.