Transversely projective structures on a transversely holomorphic foliation, II
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- by Indranil Biswas
- Conform. Geom. Dyn. 6 (2002), 61-73
- DOI: https://doi.org/10.1090/S1088-4173-02-00085-1
- Published electronically: August 7, 2002
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Abstract:
Given a transversely projective foliation $\mathcal F$ on a $C^\infty$ manifold $M$ and a nonnegative integer $k$, a transversal differential operator ${\mathcal D}_{\mathcal F}(2k+1)$ of order $2k+1$ from $N^{\otimes k}$ to $N^{\otimes (-k-1)}$ is constructed, where $N$ denotes the normal bundle for the foliation. There is a natural homomorphism from the space of all infinitesimal deformations of the transversely projective foliation $\mathcal F$ to the first cohomology of the locally constant sheaf over $M$ defined by the kernel of the operator ${\mathcal D}_{\mathcal F}(3)$. On the other hand, from this first cohomology there is a homomorphism to the first cohomology of the sheaf of holomorphic sections of $N$. 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.References
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Bibliographic Information
- Indranil Biswas
- Affiliation: School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
- MR Author ID: 340073
- Email: indranil@math.tifr.res.in
- Received by editor(s): October 22, 2001
- Received by editor(s) in revised form: June 24, 2002
- Published electronically: August 7, 2002
- © Copyright 2002 American Mathematical Society
- 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
- MathSciNet review: 1948849