Rational fibrations homogeneous spaces with positive Euler characteristics and Jacobians

Structure of Rational Open Surfaces with Non{positive Euler Characteristic

We study mainly connected conngurations of irreducible curves r i=1 C i on a nonsingular rational projective complex surface X such that the Euler characteristic (X n r i=1 C i) 0, hereby continuing a former conjecture of the author and work of Gurjar and Parameswaran. Roughly we show that any such connguration can be extended to another connguration s i=1 C i (r s) with still (X n s i=1 C i) 0...

Euler equations on homogeneous spaces and Virasoro orbits

We show that the following three systems related to various hydrodynamical approximations: the Korteweg–de Vries equation, the Camassa–Holm equation, and the Hunter–Saxton equation, have the same symmetry group and similar bihamiltonian structures. It turns out that their configuration space is the Virasoro group and all three dynamical systems can be regarded as equations of the geodesic flow ...

Relative Jacobians of Elliptic Fibrations with Reducible Fibers

We prove that if X and S are smooth varieties and f : X → S is an elliptic fibration with singular fibers curves of types IN with N ≥ 1, II, III and IV, then the relative Jacobian f̂ : MX/S → S of f , defined as the relative moduli space of semistable pure dimension one sheaves of rank 1 and degree 0 on the fibers of f , is an elliptic fibration such that all its fibers are irreducible. This ext...

Frames and Homogeneous Spaces

Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...

Convolution and Homogeneous Spaces