Transversely projective structures on a transversely holomorphic foliation, II

Author:
Indranil Biswas

Journal:
Conform. Geom. Dyn. **6** (2002), 61-73

MSC (2000):
Primary 37F75; Secondary 53B10

DOI:
https://doi.org/10.1090/S1088-4173-02-00085-1

Published electronically:
August 7, 2002

MathSciNet review:
1948849

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Abstract: Given a transversely projective foliation on a manifold and a nonnegative integer , a transversal differential operator of order from to is constructed, where denotes the normal bundle for the foliation. There is a natural homomorphism from the space of all infinitesimal deformations of the transversely projective foliation to the first cohomology of the locally constant sheaf over defined by the kernel of the operator . On the other hand, from this first cohomology there is a homomorphism to the first cohomology of the sheaf of holomorphic sections of . The composition of these two homomorphisms coincide with the infinitesimal version of the forgetful map that sends a transversely projective foliation to the underlying transversely holomorphic foliation.

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Additional Information

**Indranil Biswas**

Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India

Email:
indranil@math.tifr.res.in

DOI:
https://doi.org/10.1090/S1088-4173-02-00085-1

Received by editor(s):
October 22, 2001

Received by editor(s) in revised form:
June 24, 2002

Published electronically:
August 7, 2002

Article copyright:
© Copyright 2002
American Mathematical Society