Birational maps between Calabi-Yau manifolds associated to webs of quadrics

Details Birational maps between Calabi-Yau manifolds associated to webs of quadrics Birational maps between Calabi-Yau manifolds associated to webs of quadrics

2009-04-28

arxiv.org/abs/0904.4404v4

Mathematics

Algebraic Geometry

Scientific paper

We consider two varieties associated to a web of quadrics W in the projective space of dimension 7. One is the base locus and the second one is the double cover of the three dimensional projective space branched along the determinant surface of W. We show that small resolutions of these varieties are Calabi-Yau manifolds. We compute their Betti numbers and show that they are not birational in the generic case. The main result states that if the base locus of W contains a plane then in the generic case the two varieties are birational.

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