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June 2014 Infinitesimal Deformations and Brauer Group of Some Generalized Calabi--Eckmann Manifolds
Indranil BISWAS, Mahan MJ, Ajay Singh THAKUR
Tokyo J. Math. 37(1): 61-72 (June 2014). DOI: 10.3836/tjm/1406552431


Let $X$ be a compact connected Riemann surface. Let $\xi_1: E_1\longrightarrow X$ and $\xi_2: E_2\,\longrightarrow X$ be holomorphic vector bundles of rank at least two. Given these together with a $\lambda \in {\mathbb C}$ with positive imaginary part, we construct a holomorphic fiber bundle $S^{\xi_1,\xi_2}_{\lambda}$ over $X$ whose fibers are the Calabi--Eckmann manifolds. We compute the Picard group of the total space of $S^{\xi_1,\xi_2}_{\lambda}$. We also compute the infinitesimal deformations of the total space of $S^{\xi_1,\xi_2}_{\lambda}$. The cohomological Brauer group of $S^{\xi_1,\xi_2}_{\lambda}$ is shown to be zero. In particular, the Brauer group of $S^{\xi_1,\xi_2}_{\lambda}$ vanishes.


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Indranil BISWAS. Mahan MJ. Ajay Singh THAKUR. "Infinitesimal Deformations and Brauer Group of Some Generalized Calabi--Eckmann Manifolds." Tokyo J. Math. 37 (1) 61 - 72, June 2014.


Published: June 2014
First available in Project Euclid: 28 July 2014

zbMATH: 1330.14026
MathSciNet: MR3264514
Digital Object Identifier: 10.3836/tjm/1406552431

Primary: 14F22
Secondary: 32G05, 32Q55

Rights: Copyright © 2014 Publication Committee for the Tokyo Journal of Mathematics


Vol.37 • No. 1 • June 2014
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