Meromorphic Line Bundles and Holomorphic Gerbes

Details Meromorphic Line Bundles and Holomorphic Gerbes Meromorphic Line Bundles and Holomorphic Gerbes

2011-01-11

arxiv.org/abs/1101.2216v1

Math. Res. Lett. 18 (2011), 6, 1-14

Mathematics

Algebraic Geometry

14 pages

Scientific paper

We show that any complex manifold that has a divisor whose normalization has non-zero first Betti number either has a non-trivial holomorphic gerbe which does not trivialize meromorphicly or 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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