On the cohomology of stable map spaces

We describe an approach to calculating the cohomology rings of stable map spaces. The method we use is due to Akildiz-Carrell and employs a C^*-action and a vector field which is equivariant with respect to this C^*-action. We give an explicit description of the big Bialynicky-Birula cell of the C^*-action on Mbar_00(P^n,d) as a vector bundle on Mbar_0d. This is used to calculate explicitly the cohomology ring of Mbar_00(P^n,d) in the cases d=2 and d=3. Of particular interest is the case as n approaches infinity.Comment: 63 page

On localization in holomorphic equivariant cohomology

We prove a localization formula for a "holomorphic equivariant cohomology" attached to the Atiyah algebroid of an equivariant holomorphic vector bundle. This generalizes Feng-Ma, Carrell-Liebermann, Baum-Bott and K. Liu's localization formulas.Comment: 16 pages. Completely rewritten, new title. v3: Minor changes in the exposition. v4: final version to appear in Centr. Eur. J. Mat

Unusually long cooperative chain of seven hydrogen bonds. An alternative packing type for symmetrical phenols

Conformational flexibility in a symmetrical tris-phenol leads to close packed structures that are also characterised by an extended though finite cooperative chain of hydrogen bonds

Numerical Simulation of a possible origin of the positive radial metallicity gradient of the thick disk

We analyze the radial and vertical metallicity and [alpha/Fe] gradients of the disk stars of a disk galaxy simulated in a fully cosmological setting with the chemodynamical galaxy evolution code, GCD+. We study how the radial abundance gradients vary as a function of height above the plane and find that the metallicity ([alpha/Fe]) gradient becomes more positive (negative) with increasing height, changing sign around 1.5 kpc above the plane. At the largest vertical height (2 2 kpc at the outer region, because of the lower gravitational restoring force of the disk, i.e. flaring. As a result, the fraction of younger stars with higher metallicity due to the age-metallicity relation becomes higher at the outer radii, which makes the median metallicity higher at the outer radii. Combining this result with the recently observed age-metallicity and age-velocity dispersion relation for the Milky Way thick disk stars suggested by Haywood et al. (2013), we argue that the observed (small) positive radial metallicity gradient at large heights of the Milky Way disk stars can be explained by the flaring of the younger thick and/or thin disk stars

Evidence for the characterisation of the C-H …∏ interaction as a weak hydrogen bond: toluene and chlorobenzene solvates of 2,3,7,8-tetraphenyl-1,9,10-anthyridine

The crystal structures of the toluene and chlorobenzene solvates of 2,3,7,8-tetraphenyl-1,9,10-anthyridine are nearly identical save for differences in the mode of solvent inclusion; these differences have an important bearing on the nature of the C-H … ∏ interactions in these structures

Residues and World-Sheet Instantons

We reconsider the question of which Calabi-Yau compactifications of the heterotic string are stable under world-sheet instanton corrections to the effective space-time superpotential. For instance, compactifications described by (0,2) linear sigma models are believed to be stable, suggesting a remarkable cancellation among the instanton effects in these theories. Here, we show that this cancellation follows directly from a residue theorem, whose proof relies only upon the right-moving world-sheet supersymmetries and suitable compactness properties of the (0,2) linear sigma model. Our residue theorem also extends to a new class of "half-linear" sigma models. Using these half-linear models, we show that heterotic compactifications on the quintic hypersurface in CP^4 for which the gauge bundle pulls back from a bundle on CP^4 are stable. Finally, we apply similar ideas to compute the superpotential contributions from families of membrane instantons in M-theory compactifications on manifolds of G_2 holonomy.Comment: 47 page

Degenerate flag varieties: moment graphs and Schr\"oder numbers

We study geometric and combinatorial properties of the degenerate flag varieties of type A. These varieties are acted upon by the automorphism group of a certain representation of a type A quiver, containing a maximal torus T. Using the group action, we describe the moment graphs, encoding the zero- and one-dimensional T-orbits. We also study the smooth and singular loci of the degenerate flag varieties. We show that the Euler characteristic of the smooth locus is equal to the large Schr\"oder number and the Poincar\'e polynomial is given by a natural statistics counting the number of diagonal steps in a Schr\"oder path. As an application we obtain a new combinatorial description of the large and small Schr\"oder numbers and their q-analogues.Comment: 25 page