Fiberwise stable bundles on elliptic threefolds with relative Picard number one

Details Fiberwise stable bundles on elliptic threefolds with relative Picard number one Fiberwise stable bundles on elliptic threefolds with relative Picard number one

2006-01-10

arxiv.org/abs/math/0601234v1

C. R. Acad. Sci. Paris, Ser. I 334 (2002), 469-472

Mathematics

Algebraic Geometry

4 pages, non-standard format used

Scientific paper

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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