We discuss aspects of the dictionary between brane configurations in del Pezzo geometries and dibaryons in the dual superconformal quiver gauge theories. The basis of fractional branes defining the quiver theory at the singularity has a K-theoretic dual exceptional collection of bundles which can be used to read off the spectrum of dibaryons in the weakly curved dual geometry. Our prescription ...

Small codimensional embedded manifolds defined by equations of small degree are Fano and covered by lines. They are complete intersections exactly when the variety of lines through a general point is so and has the right codimension. This allows us to prove the Hartshorne Conjecture for manifolds defined by quadratic equations and to obtain the list of such Hartshorne manifolds. Using the geome...

Given the projection of a su cient number of points it is pos sible to algebraically eliminate the camera parameters and obtain view invariant functions of image coordinates and space coordinates These single view invariants have been introduced in the past however they are not as well understood as their dual multi view tensors In this paper we revisit the dual tensors bilinear trilinear and q...

Using a nonsymmetric duality for abstract continuous convex control problems opti-mality conditions are derived for calculating the primal and dual solutions in the case of linear on state depending dual operators. Functional and pointwise conditions are considered. Subject: 49K22, 49K27, 49N15, 90C42. Keywords: abstract optimal control , nonsymmetric duality, suucient conditions of optimality,...

It was recently shown by Witten that B-type open topological string theory with the supertwistor space CP 3|4 as a target space is equivalent to holomorphic Chern-Simons (hCS) theory on the same space. This hCS theory in turn is equivalent to self-dual N=4 super Yang-Mills (SYM) theory in four dimensions. We review the supertwistor description of self-dual and anti-self-dual N -extended SYM the...

Starting from the classification of 6–dimensional real Drinfeld doubles and their decomposition into Manin triples we construct 3–dimensional Poisson–Lie T–dual or more precisely T–plural sigma models. Of special interest are those that are conformally invariant. Examples of models that satisfy vanishing β–function equations with zero dilaton are presented and their duals are calculated. It tur...