Log BPS numbers of log Calabi-Yau surfaces

Homogeneous fibrations on log Calabi-Yau varieties

Weprove a structure theorem for the Albanese maps of varieties withQ-linearly trivial log canonical divisors. Our start point is the action of a nonlinear algebraic group on a projective variety.

4 Ju n 20 11 MIRROR SYMMETRY FOR LOG CALABI - YAU SURFACES I

Bell Numbers, Log-concavity, and Log-convexity

Let fb k (n)g 1 n=0 be the Bell numbers of order k. It is proved that the sequence fb k (n)=n!g 1 n=0 is log-concave and the sequence fb k (n)g 1 n=0 is log-convex, or equivalently, the following inequalities hold for all n 0, 1 b k (n + 2)b k (n) b k (n + 1) 2 n + 2 n + 1 : Let f(n)g 1 n=0 be a sequence of positive numbers with (0) = 1. We show that if f(n)g 1 n=0 is log-convex, then (n)(m) (n...

The spectrum of BPS branes on a noncompact Calabi-Yau

We begin the study of the spectrum of BPS branes and its variation on lines of marginal stability on OIP2(−3), a Calabi-Yau ALE space asymptotic to C/Z3. We show how to get the complete spectrum near the large volume limit and near the orbifold point, and find a striking similarity between the descriptions of holomorphic bundles and BPS branes in these two limits. We use these results to develo...

Non-BPS D-branes on a Calabi-Yau Orbifold

A system containing a pair of non-BPS D-strings of type IIA string theory on an orbifold, representing a single D2-brane wrapped on a nonsupersymmetric 2-cycle of a Calabi-Yau 3-fold with (h(1,1), h(1,2)) = (11,11), is analyzed. In certain region of the moduli space the configuration is stable. We show that beyond the region of stability the system can decay into a pair of non-BPS D3-branes. At...