On nodal Enriques surfaces and quartic double solids
Abstract
We consider the class of singular double coverings $X \to \PP^3$ ramified in the degeneration locus $D$ of a family of 2dimensional quadrics. These are precisely the quartic double solids constructed by Artin and Mumford as examples of unirational but nonrational conic bundles. With such quartic surface $D$ one can associate an Enriques surface $S$ which is the factor of the blowup of $D$ by a natural involution acting without fixed points (such Enriques surfaces are known as nodal Enriques surfaces or Reye congruences). We show that the nontrivial part of the derived category of coherent sheaves on this Enriques surface $S$ is equivalent to the nontrivial part of the derived category of a minimal resolution of singularities of $X$.
 Publication:

arXiv eprints
 Pub Date:
 December 2010
 arXiv:
 arXiv:1012.3530
 Bibcode:
 2010arXiv1012.3530I
 Keywords:

 Mathematics  Algebraic Geometry
 EPrint:
 18 pages