Mathematical Research Letters

Volume 18 (2011)

Number 6

Meromorphic Line Bundles and Holomorphic Gerbes

Pages: 1071 – 1084

DOI: http://dx.doi.org/10.4310/MRL.2011.v18.n6.a3

Authors

Edoardo Ballico

Oren Ben-Bassat

Abstract

We will consider the relationship of the topology of (normalizations of) divisors inside complex manifolds with holomorphic gerbes and meromorphic line bundles on these manifolds. If the normalization of the divisor has non-zero first Betti number then the manifold has either (1) a non-trivial holomorphic gerbe which does not trivialize meromorphically or (2) a meromorphic line bundle not equivalent to any holomorphic line bundle. Similarly, higher Betti numbers of divisors correspond to higher gerbes or meromorphic gerbes. We give several new examples.

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