10 research outputs found
Stable sheaves on elliptic fibrations
We characterize the subscheme of the moduli space of torsion-free sheaves on
an elliptic surface which are stable of relative degree zeero (with respect to
a polarization of type aH+bf, H being the section and f the elliptic fibre)
which is isomorphic, via the relative Fourier-Mukai transform, with the
relative compactified Simpson Jacobian of the family of those curves D in the
surface which are flat over the base of the elliptic fibration. This
generalizes and completes earlier constructions due to Friedman, Morgan and
Witten. We also study the relative moduli scheme of sheaves whose restriction
to each fibre is torsion-free and semistable of rank n and degree zero for
higher dimensional elliptic fibrations. The relative Fourier-Mukai transform
induces an isomorphic between this relative moduli space and the relative n-th
symmetric product of the fibration.Comment: AMS-LaTeX, 18 pages, XY-pic; new title, some modifications; final
version as accepted in J. Geom. Phy
D-brane Deconstructions in IIB Orientifolds
With model building applications in mind, we collect and develop basic
techniques to analyze the landscape of D7-branes in type IIB compact Calabi-Yau
orientifolds, in three different pictures: F-theory, the D7 worldvolume theory
and D9-anti-D9 tachyon condensation. A significant complication is that
consistent D7-branes in the presence of O7^- planes are generically singular,
with singularities locally modeled by the Whitney Umbrella. This invalidates
the standard formulae for charges, moduli space and flux lattice dimensions. We
infer the correct formulae by comparison to F-theory and derive them
independently and more generally from the tachyon picture, and relate these
numbers to the closed string massless spectrum of the orientifold
compactification in an interesting way. We furthermore give concrete recipes to
explicitly and systematically construct nontrivial D-brane worldvolume flux
vacua in arbitrary Calabi-Yau orientifolds, illustrate how to read off D-brane
flux content, enhanced gauge groups and charged matter spectra from tachyon
matrices, and demonstrate how brane recombination in general leads to flux
creation, as required by charge conservation and by equivalence of geometric
and gauge theory moduli spaces.Comment: 49 pages, v2: two references adde