Stable Sheaves Over K3 Fibrations

Details Stable Sheaves Over K3 Fibrations Stable Sheaves Over K3 Fibrations

2008-02-20

arxiv.org/abs/0802.2903v3

Mathematics

Algebraic Geometry

21 pages latex, final version to be published in Internat. J. Math

Scientific paper

We construct stable sheaves over K3 fibrations using a relative Fourier-Mukai transform which describes the sheaves in terms of spectral data similar to the construction for elliptic fibrations. On K3 fibered Calabi-Yau threefolds we show that the Fourier-Mukai transform induces an embedding ion of the relative Jacobian of spectral line bundles on spectral covers into the moduli space of sheaves of given invariants. This makes the moduli space of spectral sheaves to a generic torus fibration over the moduli space of curves of given arithmetic genus on the Calabi-Yau manifold.

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