0. Introduction i. Weighted projective space i.i. Notations 1.2. Interpretations 1.3. The first properties 1.4. Cohomology of 0F(n) 1.5. Pathologies 2. Bott's theorem 2.1. The sheaves ~(n) 2.2. Justifications 2.3. Cohomology of ~$(n) 3. Weighted complete intersections 3.1. Quasicones 3.2. Complete intersections 3.3. The dualizing sheaf 3.4. The Poincare series 3.5. Examples 4. The Hodge structu...

Many separable dynamic incentive problems have primal recursive formulations in which utility promises serve as state variables. We associate families of dual recursive problems with these by selectively dualizing constraints. We make transparent the connections between recursive primal and dual approaches, relate value iteration under each and give conditions for such value iteration to be con...

We carefully develop the theory of Serre duality and dualizing sheaves. We differ from the approach in [12] in that the use of spectral sequences and the Yoneda pairing are emphasized to put the proofs in a more systematic framework. As applications of the theory, we discuss the RiemannRoch theorem for curves and Bott’s theorem in representation theory (following [8]) using the algebraic-geomet...

Let R be a commutative noetherian local ring with completion b R. When R has the approximation property, we prove an approximation result for complexes with finitely generated homology. This is used to investigate descent of semidualizing complexes from b R to R. We show that, if R has the approximation property, then there is a bijective correspondence between semidualizing b R-complexes and s...

The N = 1 superspace generalization of the 3-brane action in 6 dimensions with partially broken N = 2 supersymmetry can be constructed using N = 1 chiral, complex linear, or real linear superfields. The physical scalars of these multiplets give equivalent descriptions of the two transverse coordinates. The second supersymmetry is realized nonlinearly in all these actions. We derive the superspa...

We prove that the higher direct images of the dualizing sheaf of a Lagrangian fibration between smooth projective manifolds are isomorphic to the cotangent bundles of base space. As a corollary, we obtain that every Hodge number of the base space of a fibre space of an irreducible symplectic manifold is the same to that of a projective space if the base space is smooth.

This paper is a sequel to the one in this same session which surveys recent results on the role of convexity in Hamilton-Jacobi theory. We describe here how value functions in optimal control can be represented as upper and lower envelopes involving so-called kernel functions. Particularly noteworthy is a lower envelope formula given in terms of the dualizing kernel, which is a value function i...

By our count, 245 projective planes of order less than 32 are currently known. This list is dominated by the 193 known planes of order 25. Most of these are either translation planes or Hughes planes, or planes obtained from these by the well-known process of repeatedly dualizing and deriving. We describe two new planes obtainable by the quite different method of ‘lifting quotients’. 2000 Mathe...