We derive the dual conformal field theory Virasoro algebras from the algebra of conserved diffeomorphism charges for a large class of Abelian Kaluza–Klein black holes. Under certain conditions, such as non-vanishing electric and magnetic monopole charges, the Kaluza–Klein black holes have a Reissner– Nordstrom spacetime structure. For the non-extremal charged Kaluza–Klein black holes, we use th...

These lecture notes treat some current aspects of two closely interrelated topics from the theory of convex polytopes: the shapes of f -vectors, and extremal constructions. The study of f -vectors has had huge successes in the last forty years. The most fundamental one is undoubtedly the “g-theorem,” conjectured by McMullen in 1971 and proved by Billera & Lee and Stanley in 1980, which characte...

We prove that, for every r ≥ 2, the moduli space M X (r; c1, c2) of rank r stable vector bundles with Chern classes c1 = rH and c2 = 1 2 (3r 2 − r) on a nonsingular cubic surface X ⊂ P3 contains a nonempty smooth open subset formed by ACM bundles, i.e. vector bundles with no intermediate cohomology. The bundles we consider for this study are extremal for the number of generators of the correspo...

It is known that any local maximizer of an explicitly quasiconvex realvalued function is actually a global minimizer, whenever it belongs to the intrinsic core of the function’s domain. We show that a similar property holds for componentwise explicitly quasiconvex vector-valued functions, with respect to the optimality concepts of ideal, strong and weak efficiency. These new results are applied...

It is shown that extremal magnetic black hole solutions of N = 2 supergravity coupled to vector multiplets X with a generic holomorphic prepotential F (X) can be described as supersymmetric solitons which interpolate between maximally symmetric limiting solutions at spatial infinity and the horizon. A simple exact solution is found for the special case that the ratios of the X are real, and it ...

It is shown that every cyclic split system S defined on an n-set with #S > 2kn− (2k+1 2 ) for some k ≤ n−1 2 always contains a subset of k+1 pairwise incompatible splits provided one has min(k, n−(2k+1)) ≤ 3. In addition, some related old and new conjectures are also discussed.

Let X be a smooth, complete toric variety. Let A1(X) be the group of algebraic 1-cycles on X modulo numerical equivalence and N1(X) = A1(X) ⊗Z Q . Consider in N1(X) the cone NE(X) generated by classes of curves on X. It is a well-known result due to M. Reid [11] that NE(X) is closed, polyhedral and generated by classes of invariant curves on X. The variety X is projective if and only if NE(X) i...