We display explicit half-conformally-flat metrics on the connected sum of any number of copies of the complex projective plane. These metrics are obtained from magnetic monopoles in hyperbolic 3-space by an analogue of the Gibbons-Hawking ansatz, and are conformal compactifications of asymptotically-flat, scalar-flat Kahler metrics on «-fold blow-ups of C . The corresponding twistor spaces are ...

Let M be a compact irreducible Hermitian symmetric space and write M = G/K, with G the group of holomorphic isometries of M and K the stability group of the point of 0 ∈ M . We determine the maximal dimension of a complex projective space embedded in M as a totally geodesic submanifold. AMS Subject Classification: 14L35, 22F30, 20G05 Introduction Let M be a simply connected compact complex mani...

The higher direct image complex of a coherent sheaf (or finite complex of coherent sheaves) under a projective morphism is a fundamental construction that can be defined via a Cech complex or an injective resolution, both inherently infinite constructions. Using exterior algebras and relative versions of theorems of Beilinson and Bernstein-Gel’fand-Gel’fand, we give an alternate description in ...