Complex methods in real integral geometry

Eastwood, Michael. "Complex methods in real integral geometry." Proceedings of the 16th Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 1997. [55]-71. <http://eudml.org/doc/221095>.

@inProceedings{Eastwood1997,
abstract = {This is an exposition of a general machinery developed by M. G. Eastwood, T. N. Bailey, C. R. Graham which analyses some real integral transforms using complex methods. The machinery deals with double fibrations $M\subset \Omega \{\overset\{\eta \}\{\rightarrow \}\leftarrow \} \widetilde\{\Omega \}@>\tau >> X$$(\Omega $ complex manifold; $M$ totally real, real-analytic submanifold; $\widetilde\{\Omega \}$ real blow-up of $\Omega $ along $M$; $X$ smooth manifold; $\tau $ submersion with complex fibers of complex dimension one). The first result relates through an exact sequence the space of sections of a holomorphic vector bundle $V$ on $\Omega $, restricted to $M$, to its Dolbeault cohomology on $\Omega $, resp. its lift to $\widetilde\{\Omega \}$. The second result proves a spectral sequence relating the involutive cohomology of the lift of $V$ to its push-down to $X$. The machinery is illustrated by its application to $X$-ray transform.},
author = {Eastwood, Michael},
booktitle = {Proceedings of the 16th Winter School "Geometry and Physics"},
keywords = {Proceedings; Winter school; Srní (Czech Republic); Geometry; Physics},
location = {Palermo},
pages = {[55]-71},
publisher = {Circolo Matematico di Palermo},
title = {Complex methods in real integral geometry},
url = {http://eudml.org/doc/221095},
year = {1997},
}

TY - CLSWK
AU - Eastwood, Michael
TI - Complex methods in real integral geometry
T2 - Proceedings of the 16th Winter School "Geometry and Physics"
PY - 1997
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [55]
EP - 71
AB - This is an exposition of a general machinery developed by M. G. Eastwood, T. N. Bailey, C. R. Graham which analyses some real integral transforms using complex methods. The machinery deals with double fibrations $M\subset \Omega {\overset{\eta }{\rightarrow }\leftarrow } \widetilde{\Omega }@>\tau >> X$$(\Omega $ complex manifold; $M$ totally real, real-analytic submanifold; $\widetilde{\Omega }$ real blow-up of $\Omega $ along $M$; $X$ smooth manifold; $\tau $ submersion with complex fibers of complex dimension one). The first result relates through an exact sequence the space of sections of a holomorphic vector bundle $V$ on $\Omega $, restricted to $M$, to its Dolbeault cohomology on $\Omega $, resp. its lift to $\widetilde{\Omega }$. The second result proves a spectral sequence relating the involutive cohomology of the lift of $V$ to its push-down to $X$. The machinery is illustrated by its application to $X$-ray transform.
KW - Proceedings; Winter school; Srní (Czech Republic); Geometry; Physics
UR - http://eudml.org/doc/221095
ER -