We consider two varieties associated to a web of quadrics W in P-7. One is the base locus and the second one is the double cover of P-3 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. (C) 2012 Elsevier Inc. All rights reserved.
- Webs of quadrics
- Calabi-Yau manifolds