CY Principal Bundles over Compact Kähler Manifolds

Jingyue Chen Brandeis University Bong H. Lian Brandeis University


A CY bundle on a compact complex manifold X was a crucial ingredient in constructing differential systems for period integrals in \cite{LY}, by lifting line bundles from the base X to the total space. A question was therefore raised as to whether there exists such a bundle that supports the liftings of all line bundles from X , simultaneously. This was a key step for giving a uniform construction of differential systems for arbitrary complete intersections in X . In this paper, we answer the existence question in the affirmative if X is assumed to be K\"ahler, and also in general if the Picard group of X is assumed to be free. Furthermore, we prove a rigidity property of CY bundles if the principal group is an algebraic torus, showing that such a CY bundle is essentially determined by its character map.
Principal Bundles, Kähler Manifolds
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  title={CY Principal Bundles over Compact Kähler Manifolds},
  author={Jingyue Chen, and Bong H. Lian},
Jingyue Chen, and Bong H. Lian. CY Principal Bundles over Compact Kähler Manifolds. 2014.
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