ar X iv : m at h / 05 02 57 3 v 6 [ m at h . A G ] 1 4 M ay 2 00 6 ON DEFORMATIONS OF FLAG

ar X iv : m at h / 05 02 57 3 v 7 [ m at h . A G ] 8 A ug 2 00 6 ON DEFORMATIONS OF FLAG MANIFOLDS WITH

Any (global) kähler deformation of a flag manifold F with b2 = 1 is biholomorphic to F .

ar X iv : m at h / 06 05 35 5 v 1 [ m at h . G R ] 1 3 M ay 2 00 6 Axes in Outer Space

ar X iv : m at h / 06 05 64 5 v 1 [ m at h . A G ] 2 4 M ay 2 00 6 ON NORI ’ S FUNDAMENTAL GROUP SCHEME

The aim of this note is to give two structure theorems on Nori’s fundamental group scheme of a proper connected variety defined over a perfect field and endowed with a rational point.

ar X iv : m at h / 05 05 66 9 v 1 [ m at h . D G ] 3 1 M ay 2 00 5 INVARIANT RIEMANNIAN METRICS AND f - STRUCTURES ON FLAG MANIFOLDS

It turns out that if a reductive complement m of a homogeneous reductive space G/H possesses a number of properties (including its decomposability into an orthogonal sum of three Ad(H)-invariant irreducible subspaces) then there exists a simple way of determining whether an f -structure F on this space belongs to the classes G1f , NKf and Kill f of generalized Hermitian geometry with respect to...

ar X iv : m at h / 06 05 36 9 v 1 [ m at h . A G ] 1 4 M ay 2 00 6 Vanishing Cycles and Thom ’ s a f Condition ∗

We give a complete description of the relationship between the vanishing cycles of a complex of sheaves along a function f and Thom’s af condition.