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Fiberwise stable bundles on elliptic threefolds with relative Picard number one

Andrei Caldararu
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Abstract

We show that fiberwise stable vector bundles are preserved by relative Fourier-Mukai transforms between elliptic threefolds with relative Picard number one. Using these bundles we define new invariants of elliptic fibrations, and we relate the invariants of a space with those of a relative moduli space of stable sheaves on it. As a byproduct, we calculate the intersection form of a certain new example of an elliptic Calabi-Yau threefold.

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Andrei Caldararu. 2006-01-10. Fiberwise stable bundles on elliptic threefolds with relative Picard number one. https://arxiv.org/abs/math/0601234

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