Gorenstein formats, canonical and Calabi-Yau threefolds
  We extend the known classification of threefolds of general type that are complete intersections to various classes of non-complete intersections, and find other classes of polarised varieties, including Calabi-Yau threefolds with canonical singularities, that are not complete intersections. Our methods apply more generally to construct orbifolds described by equations in given Gorenstein formats. 
Gavin Brown, Alexander Kasprzyk, Lei Zhu
math.AG