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Stability of vector bundles from F-theory. (English) Zbl 0953.14025

Summary: We use a recently proposed construction of stable holomorphic vector bundles \(V\) on elliptically fibered Calabi-Yau \(n\)-folds \(Z_n\) in terms of F-theory compactifications on local singularities to describe stability conditions on \(V\). Specifically, the requirement that the F-theory compactification manifold is Calabi-Yau implies a stability criterion on \(V\) which is formulated in terms of the existence of holomorphic sections of certain line bundles.

MSC:

14J32 Calabi-Yau manifolds (algebro-geometric aspects)
81T99 Quantum field theory; related classical field theories
14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
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