By a holomorphic homogeneous symplectic transformation of T* X (for X = cN ), we interchange the conormal bundle T~ X to a higher codimensional submanifold M with the conormal bundle T* X to a hypersurface IV1 of X. For an analytic disc A "attached" to M we are able to find M a section A* C T*X with zrA* = A, attached to T~4X, such that A := zrx(A* ) is an analytic disc "attached" to ,~I. By this procedure of "transferring'" analytic discs, we get the higher codimensional version of our criteria of[5] on holomorphic extension of CR functions (with [51 being on its hand the main tool of the present pmof). Thus, let W be a wedge of X with generic edge M and assume that there exists an analytic disc contained in M U W, tangent to M at a boundary point Zo E O A, and not contained in M in any neighborhood of zo. Then germs ofholomorphic functions on W at Zo extend to a full neighborhood of zo.
Analytic discs under sympletic transforms
BARACCO, LUCA;ZAMPIERI, GIUSEPPE
2006
Abstract
By a holomorphic homogeneous symplectic transformation of T* X (for X = cN ), we interchange the conormal bundle T~ X to a higher codimensional submanifold M with the conormal bundle T* X to a hypersurface IV1 of X. For an analytic disc A "attached" to M we are able to find M a section A* C T*X with zrA* = A, attached to T~4X, such that A := zrx(A* ) is an analytic disc "attached" to ,~I. By this procedure of "transferring'" analytic discs, we get the higher codimensional version of our criteria of[5] on holomorphic extension of CR functions (with [51 being on its hand the main tool of the present pmof). Thus, let W be a wedge of X with generic edge M and assume that there exists an analytic disc contained in M U W, tangent to M at a boundary point Zo E O A, and not contained in M in any neighborhood of zo. Then germs ofholomorphic functions on W at Zo extend to a full neighborhood of zo.Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.