We provide a classification theorem for compact stable minimal immersions (CSMI) of codimension 1 or dimension (codimension and 2 2) in the product complex (quaternionic) projective space with any other Riemannian manifold. characterize as only CSMI two spaces. As an application, we rank one symmetric space.

We show this Chow ring is Z ⊕ Z. We do this by partitioning the space into 2n subvarieties each of which is fibered over Gl(2n − 2, C)/SO(2n − 2, C).

We look at general brane worlds in six-dimensional Einstein-Gauss-Bonnet gravity. We find the general matching conditions for the brane world, which remarkably give precisely the four-dimensional Einstein equations for the brane, even when the extra dimensions are noncompact and have infinite volume. Relaxing regularity of the curvature in the vicinity of the brane, or having a thick brane, giv...

We prove Sturmfels’ conjecture that toric varieties of codimension two have no other flat deformations than those obtained by Gröbner basis theory.

Hyperkähler embeddings and holomorphic symplectic geometry I. 0. Introduction. In this paper we are studying complex analytic subvarieties of a given Kähler manifold which is endowed with a holomorphic symplectic structure. By Calabi-Yau theorem, the holomorphically symplectic Kähler mani-folds can be supplied with a Ricci-flat Riemannian metric. This implies that such manifolds are hyperkähler...

We confirm a conjecture of Bernstein-Lunts which predicts that the characteristic variety of a generic polynomial vector field has no homogeneous involutive subvarieties besides the zero section and subvarieties of fibers over singular points.

We notice that, for branes wrapped on complex analytic subvarieties, the algebraic-geometric version of K-theory makes the identification between brane-antibrane pairs and lower-dimensional branes automatic. This is because coherent sheaves on the ambient variety represent gauge bundles on subvarieties, and they can be put in exact sequences (pro-jective resolutions) with sheaves corresponding ...

The question of characterizing the lattices of subvarieties of a variety of universal algebras seems to be very difficult. Some years ago a conjecture was that a lattice is isomorphic to the lattice of all extensions of an equational theory (or dually isomorphic to the lattice of subvarieties of a variety) iff it is algebraic and its greatest element is compact. In [2] and [3] W. Lampe proved t...

A local uniqueness property of holomorphic functions on realanalytic nowhere minimal CR submanifolds of higher codimension is investigated. A sufficient condition called almost minimality is given and studied. A weaker necessary condition, being contained a possibly singular real-analytic Levi-flat hypersurface is studied and characterized. This question is completely resolved for algebraic sub...