PROJECTIVELY FLAT IMMERSIONS OF HERMITIAN SYMMETRIC SPACES OF COMPACT TYPE

Projective Ranks of Compact Hermitian Symmetric Spaces

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...

74 the Deformation Spaces of Projectively Flat

Nonexistence of Arithmetic Fake Compact Hermitian Symmetric Spaces of Types

1.1. Let G be a noncompact connected real semi-simple Lie group with trivial center and with no nontrivial compact connected normal subgroups, and g be its Lie algebra. The group Aut(G) (=Aut(g)) of automorphisms of G is a Lie group with finitely many connected components, and G is its identity component. We will denote the identity component of Aut(G) in the Zariski-topology by Int(G). Let X b...

On Secant Varieties of Compact Hermitian Symmetric Spaces

We show that the secant varieties of rank three compact Hermitian symmetric spaces in their minimal homogeneous embeddings are normal, with rational singularities. We show that their ideals are generated in degree three with one exception, the secant variety of the 21-dimensional spinor variety in P, whose ideal is generated in degree four. We also discuss the coordinate ring of secant varietie...

Unitarity of Strings and Non-compact Hermitian Symmetric Spaces

If G is a simple non-compact Lie Group, withK its maximal compact subgroup, such that K contains a one-dimensional center C, then the coset space G/K is an Hermitian symmetric non-compact space. SL(2,R)/U(1) is the simplest example of such a space. It is only when G/K is an Hermitian symmetric space that there exists unitary discrete representations of G. We will here study string theories defi...